Differential equation Definition and 1000 Threads

Homework Statement Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η, where θ=(T-T0)/(Ts-T0) EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be...

Homework Statement y3(dy/dx) = (y4 + 1)cosx 2. The attempt at a solution I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy. How should...

Homework Statement A cylindrical tank, with a diameter Db, open to the atmosphere, is drained through an orifice in the bottom of the tank with a diameter Do. The speed of the fluid flowing through the orifice is given by v = \sqrt{2gh}, where h is the height of the liquid measured from the...

Homework Statement Consider a system composed of two species X and Y with fractional populations x and y, respectively, where x+y=1. The two species interact in such a way that the differential equation for x is: \begin{equation} \frac{dx}{dt}=xyA_{0}e^{-\alpha t} \end{equation} where $A_{0}$...

Homework Statement Verify that the functions y1(x) = x and y2(x) = 1/x are solutions of the differential equation y'' + (1/x)y' - (1/x2)y = 0 on I = (0,∞). Show that y1(x), y2(x) is a basis of the solution space of the differential equation. The Attempt at a Solution For the first part I'll...

Homework Statement The differential equation is xy'-2y= x3ex Check the solution y=x2 ex Homework Equations Just plug in The Attempt at a Solution y' = x2ex + 2xex Having problem solving for x.

Homework Statement [/B] A shark will in the direction of the most rapidly increasing concentration of blood in water. Suppose a shark is at a point x_0,y_0 when it first detects blood in the water. Find an equation for the path that the shark will follow by setting up and solving a...

What is the general method for solving a differential equation of the form \begin{equation} \frac{\partial^{2}z}{\partial x^{2}}+\frac{\partial^{2}z}{\partial y\partial x}=C\end{equation} where C is a constant.

Homework Statement Solve for y using the substitution: z = 1/(y^5) dy/dx + y/x = (y^6)(x^3) Homework Equations (dz/dx) = (dz/dy) x (dy/dx) The Attempt at a Solution I formed an equation for dz/dx but cannot separate the variables in order to integrate. Can someone tell me where I've gone...

Hello everyone; i'd like some help in this problem : i want to solve num this differential equation { y"(t)+t*cos(y)=y } by the Taylor method second order expansion. i first have to make this a first order differential equation by taking this vector Z=[y' y] then we have Z'=[y" y'] which equal...

Homework Statement Find the distance which an object moves in time t if it starts from rest and has an acceleration d^2x/dt^2 = ge^-kt. Show that for small t the result is approx "x=(gt^2)/2" and show that for very large t, the speed is approximately constant. the constant is called the...

Hey! :o I want to find the solution of the following initial value problem: $$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$ using Green's theorem but I got stuck... I found the following example in my notes...

Hello! (Wave) The following differential equation is given: $$(1-x^2)y''-xy'+p^2y=0, p \in \mathbb{R}$$ Find the general solution of the differential equation at the interval $(-1,1)$ (with the method of power series). Are there solutions of the differential equation that are polynomials...

I'm trying to build a circuit to solve the differential equation x''+2x'+x = f(t), where f(t) is a sine wave with frequency 5Hz and amplitude 0.5V. I am supposed to get a sine/cosine wave (as the diff. eq is just the same as the ove governing spring-mass forced oscillation) as solution, but...

Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...

I have a second order differential equation of the form (theta is a function of time): \theta ''=F\left(\theta ,\theta '\right) Turning them to two first order equations I get: \begin{cases} \theta '\:=\omega \\ \omega '=F\left(\theta ,\omega \right) \end{cases} And here's the algorithm...

Homework Statement Show that the radial eigenfunction unr,l is a solution of the differential equation: ħ2/2me×d2unr,l/dr2+[l(l+1)ħ2/2mer2 - e2/4πε0r]unr,l=Enr,lunr,lHomework Equations The radial function is R(r)=u(r)/r, so that the expression on the RHS is E×u. The Attempt at a Solution I know...

Homework Statement dy/dx=2xcos(y)-xy^3[/B]Homework EquationsThe Attempt at a Solution dy/dx=2xcos(y)-xy^3=x(2cosy-y^3) dy/(2cosy-y^3)=xdx [/B] I can not integrate the left side of the equation. Can someone help me please?

Homework Statement x(d^2y/dx^2)+dx/dt+xy=0 Homework EquationsThe Attempt at a Solution At first I thought it was an ODE, but then I found out the derivative was respect to to variables x and t. I am not sure if it is an ODE or PDE. What are the dependent and independent variables in the...

Homework Statement - The force acting on a particle m = 3kg is given by the following force equation: F = (v/9)(3 - x2), the particle begins at a position of x = 1m with a speed of v = 0 m/s at time t = 0s. Find the displacement of the particle at time t = 5 s. Homework Equations F =...

In my multivariable calculus class, we briefly went over Taylor polynomial approximations for functions of two variables. My professor said that the second degree terms include any of the following: $$x^2, y^2, xy$$ What surprised me was the fact that xy was listed as a nonlinear term. In...

I'm going through the solution to a problem that was assigned to my class and there's a step I don't really understand which I think is a concept I'm misunderstanding. 1. Homework Statement The curved surface of a cylinder of radius R and length L is insulated. The face at x = L is maintained...

Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2)[/B]Homework EquationsThe Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you need to take...

I am working on a simple PDE problem on full Fourier series like this: Given this piecewise function, ##f(x) = \begin{cases} e^x, &-1 \leq x \leq 0 \\ mx + b, &0 \leq x \leq 1.\\ \end{cases}## Without computing any Fourier coefficients, find any values of ##m## and ##b##, if there is any...

Consider the second-order homogeneous linear differential equation $y'' + 4y' + Ky = 0$ Find the general solution if $K = 4$ So here is what I have: $r^2 + 4r + 4 = 0 $ =$(r + 2)(r+2)$ $r=-2$ ? But I thought that you can't do this because you won't be learning anything new if you have two of...

Hello! (Wave) I am looking at the following exercise: We consider the differential equation $x^2y'+2xy+1=0$, where $0<x< +\infty$. Show that each solutions goes to $0$ while $x \to +\infty$. Find the solution $\phi$ of the above differential equation so that $\phi(2)=2 \phi(1)$. That's...

Homework Statement Given that a particle has an initial velocity v0 and then undergoes an acceleration a = - bv. , where b is a constant, obtain an expression for v = v(t) and x = x (t) [/B]Homework Equations Not sure The Attempt at a Solution If I integrate a = - b v I think I get v +...

Find $y(x)$ to satisfy y(x)=y'(x)+\int e^{2x}y(x) \, dx+\lim_{{x}\to{-\infty}}y(x) given \lim_{{x}\to{0}}y(x)=0 and \lim_{{x}\to{\ln\left({\pi/2}\right)}}y(x)=1.

Homework Statement So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!) I am asked to solve this differential equation: y''+y'-2y=0 Homework Equations I know for a second order differential equation I can solve for the roots first. If...

dy/dx = (2y-x+5)/(2x-y-4) y(1)=1

Homework Statement This is actually a problem from my physics textbook, but I think it's mostly a mathematical problem, which is why I post it here: Show that the Langevin equation 1: \frac{dv}{dt}=-\gamma v+\frac{1}{m} F'(t) is solved by 2...

Okay, so I am a team member of a college robotics team, and this year we have quite challenging theme of playing badminton with robots, so for this reason we decided to track the position of shuttlecock in air. Now our approach was to predict the final position where it will land on ground from...

Homework Statement Kindly see the attachment. Homework Equations The Attempt at a Solution As with all such questions, its in setting everything up that I'm having some trouble. I know that F = mdv/dt + vdm/dt. And also that F = R - m(t)g, but R = M0g. From here though I don't know how to...

I have J - matrix x and y - vector d [ J(x) y(x)] / dx I can multiply the matrix and vector together and then differentiate but I think for my application it would be better to find an identity like {d [ J(x) y(x)] / dx } = J(x) d y(x) / dx + d J (x) / dx y(x) I am not sure if this identity...

I saw this in http://en.wikipedia.org/wiki/Momentum_operator From equation 4 to 5, it seems that a function is canceled out from the partial derivatives, is this possible?

Homework Statement Solve (xy+y2+x2) dx -( x2 )dy = 0 Homework Equations to verify if exact http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngM/[PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngy =...

How Can we define the degree of differential equation ? What is the degree of \left(\frac{{d}^{2}y}{d{x}^{2}}\right)^{\!{2}}\left(\frac{dy}{dx}\right)^{\!{3}} +\left(\frac{dy}{dx}\right)^{\!{1}} =0 ??(Wondering)

Homework Statement I need help finding the limit of the differential equation. (dx/dt) = k(a-x)(b-x) that satisfies x(0)=0 assuming a) 0<a<b and find the limit as t->infinity of X(t) b) 0<a=b and find the limit as t->infinity of X(t) Homework Equations none The Attempt at a Solution I...

Find the general solution of the given differential equation.. (1+t^2)y' + 4ty = (1+t^2)^{-2} I'm kind of confused here on what to do... Do I want to do something like e ^{\int4t} dt and then multiply that through on both sides or do I need to do something different here..I'm not really sure...

Hello, this is a maths problem that is related to a physics problem, but I think it's best posted here due to what I'm asking about. 1. Homework Statement \frac{d^{2}q}{dt^{2}} + \frac{R}{L} \frac{dq}{dt} + \frac{1}{LC}q = 0 is a differential equation describing how charge and current change...

Homework Statement use laplace transforms to solve the differential equation y"+2y'+17y = 1 Homework Equations Initial conditions are y(0) = 0 y'(0) = 0 The Attempt at a Solution so it converts to Y(s) (s^2+2s+17) = 1/s which then ends up as; Y(s) = 1/s*1/(s^2+2s+17) i know i need to invert...

Hi all, I need to understand these differential equations specially moving from the second order to the third order because i couldn't understand how they got to the result, what was exactly the principle: $$ y'=f(x,y) $$ $$ y''=\frac{df}{dx}(x,y(x)) = f_{x}(x,y) + f_{y}(x,y)y' = f_{x}(x,y) +...

Hello everyone! 1. Homework Statement I want to model the irradiance on a fluid element while it is flowing, from a fixed(above or below) light source that has an irradiance that shows first order decay with time and from x-naught to x-infinity . here are the assumptions: -Laminar flow at...

I know: f = ma f = - GMm/r^2 a = -GM/r^2 can be easily derived, But, we've been given the differential equation of motion of gas within a star as: a = -GM/r^2 - 1/p * dP(r)/dr I was wondering where the - 1/p * dP(r)/dr term is derived from? I can't find it in my textbooks. Cheers

I want to solve Equation (1). w is a constant: \begin{eqnarray} \text{Equation (1): }\frac{dx}{dt}=1+x^2w^2\end{eqnarray} and I have been told that it is solved by (2): \begin{eqnarray} \text{Equation (2): }x(t)=\frac{Ax(0)+B}{Cx(0)+D}\end{eqnarray} Problem I believe them, but before I keep...

Ok so I tried to solve the following differential equation for y by every method (variable separable method/making to variable separable method technique/putting y/x=other variable/making homogeneous to solve equation to get y/x ).But I think I can't solve this particular equation by these...

Homework Statement solve the following differential equation using Laplace transforms: y'' + 4y' + 4y = t^2 e^{-2t}, y_0 = 0, y'_0 = 0 y_0 and y'_0 are initial conditions. Homework Equations Using L to represent the Laplace transform, we have that L(y) = Y L(y') = pY - y_0 L(y'') =...

Hello all, I am currently trying to solve a differential equation numerically. The equation is as follows: dv/dt = (u*q)/(m0-q*t) - g - (cd*ρ*A*0.5)*v2 If you haven't already guessed, it's the rocket equation with added gravity and drag. Now, I'm not even sure if that's what it's supposed to...

Homework Statement Shown in attachment The problem has been modified. All inputs and outputs are 5 gal/min. Pure water enters tank 1. Homework Equations System of equations The Attempt at a Solution Included on attachment.

This is actually a chemistry problem, but I feel it's more appropriate posted here, as I'm not having trouble with the chemistry but rather the mathematics. To avoid mixing subjects, I'll keep chemistry jargon out. We're given the formula for a component, and the problem request we give...