First order differential Definition and 103 Threads

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

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  1. J

    About simple first order differential equation

    Homework Statement dy/dx = (3x^2+4x+2)/2(y-1) , y(0)=1 Homework Equations The Attempt at a Solution I get the answer and the steps are shown: 2(y-1)dy=(3x^2+4x+2)dx and integrate both sides y^2-2y=x^3+2x^2+2x+c By initial condition, c=-1 and by solving for y, y =...
  2. T

    Separable First Order Differential Equation

    Homework Statement \frac{dy}{dx} = y \sqrt{x} , f(9) = 5 The Attempt at a Solution \int dy/y = \int \sqrt{x} dx ln |y| = \frac{2}{3} x^\frac{3}{2} + c y = e^{\frac{2}{3}x^\frac{3}{2}} + C y = Ce^{\frac{2}{3}x^\frac{3}{2}} 5 = Ce^{\frac{2}{3}9^\frac{3}{2}} 5 =...
  3. C

    Ugly first order differential equation

    Homework Statement solve the differential equation: (1+t^2)y'+4ty=(1+t^2)^-2Homework Equations μ=exp∫adt The Attempt at a Solution this problem gets quite ugly, so here goes. first question does μ=e^(1+t^2)^2
  4. J

    Linear First Order Differential Equation - Mixture Problem

    The problem and attempt at solution are typed below
  5. X

    First order differential equation

    I am asked to find the general solution to: \dfrac{dy}{dx}\sin x + y \sec x = \cos^2 x I don't quite know where I am going with this one; by simply looking at it, I can't seem to see what I would differentiate in order to get the left side and equally, I don't know if dividing through by...
  6. N

    How to solve this First Order Differential Equation?

    How to solve this differential equation? dy/dx = - (3yx^(2) + y^(2)) / (2x^(3) + 3xy) I've tried finding an integrating factor in order to make it exact, but I don't know what to do with this. The answer is given as x^(3)y^(2) + xy^(3) = c I'm so confused. I separated it...
  7. Y

    General Solution of the first order differential equation

    dy/dt + y = \infty \sumSin(nt)/n^2 n=1 Ok still a bit new with all these symbols and stuff but that is the basic jist of it. y(t) = yh(t) + yp(t) it what i thought about using to start off with, yh(t) = Acos2t + Bsin2t. Then subbing yp(t) into the differential equation. Not really...
  8. Y

    General Solution of the first order differential equation

    dy/dt + y =\infty\sumn=1Sin(nt)/n^2
  9. Y

    General Solution of the first order differential equation

    dy/dt + y = Sigma Sin(nt)/n^2
  10. S

    Substitution Methods for first order differential equations

    I have the following equation:: xy' = y + 2*sqrt(xy) I know I should either use the F(y/x) substitute or Bernoulli's method of substitution but I'm not sure how to manipulate the equation to determine which it is. If someone had some helpful tips on how to start, please let me know...
  11. C

    First order differential equation transforms

    I am to find a general solution of the system of problems below. I have done so for x(t) but am unsure how to find it for y(t)... x'=y, y'=-x x''=y=-x x''+x=0 Characteristic eq: r^2 + 1= 0, r = +/- i x(t) = A cos(t) + B sin(t) How do I go about calculating y(t), which th book shows as...
  12. S

    Understanding Separable Differential Equations and Initial Value Problems

    Homework Statement I am stuck on these two questions. The first one I can start off and finish but i cannot do the middle part and in the second question I have no idea how to start it off. Find the general solution of the following separable equations; then use the solution which obeys...
  13. M

    Solving a first order differential equation (calculus 1)

    Homework Statement dy/dx=y-e-x Homework Equations none The Attempt at a Solution According to Wolfram Alpha the solution is y = cex+.5e-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is. I tried factoring out e-x from the right...
  14. O

    Coupled first order differential equations

    I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved: x' = -i*(b*t-a*t^2)*x - i*c*y y' = -i*c*x -...
  15. D

    Nonlinear first order differential equation

    Homework Statement Solve the diferential equation: dx/dt + Rx^2 + G = 0 G constant = 10^18 R constant = 10^-10 Initial conditions x(0) = 10^8Homework Equations what approach to take? The Attempt at a Solution First I try to apply bernoulli, but since in this equation I do not have a term...
  16. K

    First order differential equation with substitution

    Homework Statement t^2 y' + 4ty - y^3 = 0 Homework Equations Hint was given in the question: substitute with v = y^-2 The Attempt at a Solution Dividing by t^2 and isolating y': t^2 y' = y^3 - 4ty y' = y^3 / t^2 - 4y/t dv/dt = 0 y = v^(-1/2) dy/dt = (-1/2)v^(-3/2) v' so...
  17. M

    First order differential equation

    find the solution for the following equation: dy(t)/dt + 3y(t) = x(t-2), t > 0 and y(0) = 0 i did it by parameterization but am unsure if it is correct. i need help especially with the limits of integration. y' + 3y = x(t-2) yh' = -3yh yh = Ce^-3t y(t) = v(t)e^-3t (ve^-3t)' =...
  18. D

    First order differential equation

    Homework Statement Hi, If x^2+1=y/(x-y'), where y'=dy/dx, find dy/dx I have tried so many ways, but I cannot seem to get the correct answer. The answers I have got previously are: i) x² + 1 = y/(x - y') (x² + 1)(x - y') = y x(x² + 1) - y'(x² + 1) = y x(x² + 1) - y = y'(x² + 1)...
  19. A

    First Order Differential Equation in Cylindrical Coordinates

    Consider cylindrical coordinates p = (x^2 + y^2)^.5  angle = arctan(y=x). Consider your curve to be specifi ed by z(p). Write down a ( first order) diff erential equation governing z(p) please help!
  20. I

    First order differential, initial value probelm

    Homework Statement In problem 11, determine by inspection at least two solutions of the given initial-value problem. Homework Equations 11. dy/dx = 3y^(2/3) , y(0)=0 The Attempt at a Solution I can't figure out what they mean by inspection, I have no examples to go off from...
  21. jegues

    First Order Differential Equation

    Homework Statement xy^{'} - 2y = x^{5} Homework Equations e^{\int P(x)dx} The Attempt at a Solution Rearranging the into the form, y^{'} - P(x)y = Q(x) So, y^{'} - \frac{2y}{x} = x^{4} Multiplying both sides by e^{\int P(x)dx} or e^{-2\int \frac{dx}{x}}, Since...
  22. M

    First order differential equations

    good day everyone. i need to know what test must i make first in dealing with differential equations.. please help me. it's hard for me to figure out whether an equation is homogeneous or exact... there are examples of exact differential equations that have same degrees for M(x,y) and...
  23. T

    First Order Differential Equation

    Homework Statement Find the general solution for: x y' - 2y = x +1 (x>0) Homework Equations None The Attempt at a Solution I have literally no idea how to start this. I've tried seperating variables but ended up with: \frac{y'-1}{2y+1} = \frac{1}{x} but that isn't solvable due to the y'-1...
  24. R

    Modeling with First Order Differential Equation

    Homework Statement A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. Find the amount of salt in the tank after 2 hours. I'm failing to figure out how to manipulate the...
  25. G

    First Order Differential Problem

    Homework Statement Show that if a and \lambda are positive constants, and b is any real number, then every solution of the equation dx/dt + ax = b*exp(-\lambda*t) has the property that x(t) --> 0 as t --> \infty The Attempt at a Solution i tried considering the cases where a = \lambda and a...
  26. R

    First order differential equation

    Homework Statement Solve the differential equation: Homework Equations 1+(x-x^2*e^(2y))(dy/dx) = 0 The Attempt at a Solution No idea how to approach this.
  27. A

    First order differential equation

    Hi I am looking for a firstorder differential eqaution which all of its solution, which there is a point that all of the solution goes thrugh Thank you Ariel
  28. E

    First order differential equation

    Homework Statement y is a function of t Homework Equations y'+ky(e^-t)=l(e^-3t) The Attempt at a Solution Considering that the equation is of the form dy/dt + p(t)y =q(t) , I have been looking for an integrating factor of the form: e^{integral[p(t)dt]}, where p(t) = ke^(-t) If I...
  29. A

    First Order Differential Equation

    Homework Statement Solve the following first order differential equation for x, \frac{dy}{dx} = 3xy + xy2 Homework Equations Methods: Separation of Variables, Define an Integrating Factor The Attempt at a Solution I have been staring at this question for a while now, hoping that...
  30. E

    First Order Differential Equation

    Ok so we are given a word problem discussing compound interest. In the first part of the question, we are given the equation: S(t) = (k/r)(e^rt -1) The next thing we are asked to do is calculate the value of r are given values of k, t, and S(t). The given values are k = 2000, t = 40, S(t) =...
  31. S

    Solving First Order Differential Equation using substitution

    Hi, Here is the equation: x+x'=5.1sin(600*t)*u(t) Our teacher gave us a hint that we should try using a substitution which is a system of sines, cosines, and looks something similar to 5.1sin(600*t)*u(t). I tried substituting: x(t)= A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)...
  32. C

    First order differential problem question

    question : As the salt KNO3 dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation dx/dt = 0.8x - 0.004x^2 if x=50 when t=0, how long will it take for an additional 50g of salt to dissolve. ok, here I'm encountering a...
  33. C

    First order differential question

    question : As the salt KNO3 dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation dx/dt = 0.8x - 0.004x^2 if x=50 when t=0, how long will it take for an additional 50g of salt to dissolve. ok, here I'm encountering the...
  34. T

    First order differential qusetion [ ]

    First order differential qusetion [urgent] Homework Statement Question 7 Homework Equations The Attempt at a Solution I can do part a) and i can begin part b, using separation of variables I get: 1/4 ln |1+2v| = ln|x| + C but how do i use this to solve equation I...
  35. V

    First Order Differential (Just identify)

    Not sure if I should have put this here or in the homework section but I am simply asking for direction on these problems. I have 5 problems to work on and my biggest problem is identifying what method to use to find the answer. I don't need help answering because it's something I'd like to...
  36. T

    First Order Differential Equation Problem

    Homework Statement A 14 lb weight attached to the end of spring stretches it 4 in. Find the equation of motion if the weight is released from rest at a point 3 inches above equilibrium position Homework Equations F=kx mx''+kx=0 The Attempt at a Solution ok I need some help just...
  37. S

    Very Tough Nonlinear First Order Differential Equation

    1. y' = a*(y^n) + c a, n and c are constants. Any idea about this problem ? How can it be solved ? i think there is no analytic solution thanks for your help in advance
  38. R

    First order differential equation help

    I have a problem solving a first order differential equation: dT/dP - C2/T = C1 Where C2 and C1 are just constants, the differential equations book I have does not address the situation of 1/T. I am trying to develop my own integrating factor but it would be nice for a little guidance.
  39. R

    Linear first order differential equation

    Homework Statement \frac{dy}{dx} = \frac{x^2}{2} + \frac{xy}{2} + \frac{3y^2}{2} + \frac{3y}{2} Homework Equations The Attempt at a Solution Don't really know were to begin. If anyone could tell me which method to use that would be great. I can't think of any way to solve this.
  40. M

    First Order Differential Equations

    Homework Statement Solve the following differential equation: y' = (y/x) + (2x^3Cos(x^2)/y). Homework Equations The Attempt at a Solution You certainly can't separate variables here and you can't put it in the form in which you can find the integrating factor. This is not a...
  41. E

    First order differential equation problem.

    Homework Statement Find the general solution of 2y(x^3+1)dy + 3x^2(1-y^2)dx = 0 Homework Equations The Attempt at a Solution So I first grouped the terms with dy or dx 2y/(1-y^2) dy = -3x^2/(x^3 +1) dx after integrating both sides and solving, I got ln (1-y^2)=...
  42. B

    First Order Differential Equations

    Homework Statement Solve the following differential equation using separation of variables (1+x)^2 y' = (1-y)^2 , y(1) = 2 Homework Equations The Attempt at a Solution haven't gotten very far in this at all :/ i've tried dividing both sides by (1+x)^2, in order to get y' on it's own...
  43. H

    Asymptotic mathcing for a first order differential equation

    The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...
  44. H

    Asymptotic mathcing for a first order differential equation

    The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...
  45. S

    Solving First Order Differential Equations - A Beginner's Guide

    I am new to to this topic, hints? y^1=x+5y The only examples are in the form dy/dx+p[x(y)]=Q[x]
  46. J

    Nonlinear First Order Differential Equations

    Hello. I am taking a self study diff e course, and I have run into a problem with no one to ask for help. Here is the problem: y\prime=1+x+y^2+xy^2 The question asks to find the general solution. I simply don't understand how to solve this problem. Here is the direction I am going in...
  47. X

    First order differential equation help

    i've derived the following differential eqn from a problem I'm working on, and i have tried in vain to solve this if anyone can give a direction where i should go our how to attack would be greatly appreciated. the eqn is I\,r= -L\dot{I}+\frac{3}{2}\mu_{0}m R^{2}\frac{z...
  48. M

    First order differential equation

    Just need a hand with this one. (dy/dx)x + 2y = x^3.ln(x) (dy/dx) = (x^3.ln(x) - 2y)/x Integrating factor = x^2 (dy/dx)x^2 + 2xy = (x^3.ln(x))x^2 yx^2 = INT[(x^3.ln(x))x^2] I'm having trouble integrating the last part to complete it. Thanks a lot and in advance for any help.
  49. G

    Solving a first order differential

    I have the following problem that i can't get the right answer to: y'+y=5sin(2t) I find the integrating factor u(t)=e^t multiply the whole function u(t) and i get (ye^t)'=5e^tsin(2t) I do integraton by parts on the second part and get 1/9 for the coefficents, in the calculator they...
  50. R

    Coupled first order differential equations

    How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.
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