Differential equation Definition and 1000 Threads

Homework Statement Obtain the solution of the differential equation x'' + w2nx = t My use of L refers to the Laplace Homework Equations The Attempt at a Solution L{x'' + w2nx = t} I decided to do the Laplace of each part individually starting with x'' L{x''} =...

Homework Statement Solve the following differential equation: Homework Equations 2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'' = - (y')^2 The Attempt at a Solution I don't know if the following is useful, but if you divide both sides by y^2, the LHS of the above becomes: (2 y...

Homework Statement Hello everybody :) Now, I have a differential equation to solve. Its a Bernoulli's type of eq. Homework Equations (2x2lny-x)y' = y The Attempt at a Solution I tried of putting it in this way: y'/y = 1/2x2lny-x and then considerin z=1/y, but it doesn't seem...

Homework Statement dL/dp = L/2, L(0) = 100. Find the solution to the differential equation, subject to the given initial condition. My textbook says the answer is L = 100ep/2, but I don't know how to get that answer (or e for that matter). Homework Equations ? The Attempt at a...

Homework Statement y' + 3y = t + exp(2t)Homework Equations The Attempt at a Solution My solution is y = t/3 + exp(-2t) -1/9 + c. The solution in the back of the book is y = cexp(-3t) + (t/3) - (1/9) + exp(-2t). How come the two solutions differ so vastly? I followed the procedure outlined in...

i tried to solve this question in all the ways i knew but it wouldn't work ..please help xy^2dy/dx + y = x^2 i tried to solve it by using linear first order differential equation technique and also by using different exact and reducable exact differential equaions... help me

Homework Statement t^2y" + 5ty' + 4y = 0 Possible solutions: y_1(t) = t^{-2} and y_2(t) = t^{-2} lntHomework Equations The Attempt at a Solution I was able to verify that y_1 was a solution, by the substituting the function, and its derivatives, into the differential equation, which...

The differential equation: y' -2ty = 1. The possible solution: y=e^{t^2} \int^6_0e^{-s^2}ds + e^{t^2}. For the integral, I employed integration by parts: Let u=e^{-s^2} \rightarrow du = -s2e^{-s^2}ds and Let dv = ds \rightarrow v=s. This lead to: [se^{-s^2}|^t_0 - \int_0^t...

I'm going to be taking a course in differential equations and I'm nervous. From previous calculus courses I know the derivative is the ratio of how one quantity changes with respect to another the integral is the area under the curve So what's a differential equation? According to here "A...

Dear All, Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system. I need to fit my experimental data to kinetic model that is a solution of coupled...

Homework Statement Find the ODE of the following (1) du/dy = -u (2) d^2u/dxdy = -du/dx Homework Equations For question 1, the answer is u= A(x)e^(-y) while for question 2, the answer is u= e^(-y)(B(X) + c(Y)) The Attempt at a Solution I've already solved the question, but...

Hello all, Would love for someone to help me get a solution for this. So, in essence I am trying to model a differential equation for the following scenario: (I am currently achieving this through Excel, but I'm certain a mathematical representation can make things more concise and...

Hi. Let me preface this by saying that I know nothing about economics. However, I learned a little bit about the concept of price elasticity of demand (that for something really elastic, if price goes up a little, demand will go down a lot), and I came across an equation relating price, demand...

Sorry I couldn't think of any more relevant title. Here's the equation: {x^2} - 3{y^2} + 6xy\frac{{dy}}{{dx}} = 0 I'm thinking of rewriting the above to \frac{{dy}}{{dx}} = \frac{{3{y^2} - {x^2}}}{{6xy}} followed by a change of variable u=y/x. But should I rule out the case when either x=0 or...

Trying to make a calculation and I ran into the following diff equation: r''=a+b/r^2 And I can't seem to remember how one would go about solving it. b = 1355041.84 r(0) = 1400 r(t) = 239.6 r'(o) = 0 r'(t) = 75.2 a = ? I'm specifically looking to find the value of the constant a...

I'm trying to find the equilibrium size of a planetesimal which is made of a material whose density is pressure dependent. (quite a mouthful) I have to solve this differential equation: y(x^2y''+2xy')+2y^2+bxy'=ax^2y^3+(xy')^2+by where a and b are constants.

Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...

So, as a result of a thought experiment, I've got a differential equation, which I can't solve: R r'' \sin \frac{r}{R} - 2 (r')^2 \cos \frac{r}{R} - R^2 \cos \frac{r}{R} \sin^2 \frac{r}{R} = 0 , R > 0 To make the matters worse, the function r(\varphi) will probably depend on multiple...

Hello, I am new here. I hope I am posting my problem at the right place. I need some urgent help regarding the following differential equation: A\frac{d^{2}y}{dx^{2}}+B\frac{dy}{dx}=f(x,\lambda)...(1) where, A and B are constants. x and \lambda are independent. I have solved...

hello ... I wanted to demonstrate the solution of a differential equation, and as I do not yet know the latex language, then I take pictures of the leaves with my solutions ... the user who wants to give more solutions is well received and is welcome ... att jefferson alexander vitola (Smile)...

Find the general solution for: \left(\left(x^2+y^2 \right)x-y \right)\,dx+\left(\left(x^2+y^2 \right)y+x \right)\,dy=0

hii, how to solve this differential equation: A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4 where A is a constant Thank you

I have a small problem in solving a Second Order Linear Constant Coefficient Differential Equation. Please see the attached image. I understand upto the point above the arrow. What I don't understand is how he got dy/dx = 9

Please find the general solution of : $xy'-2y =x^2$

I have the differential equation: 4(2x^2 + xy) \frac{dy}{dx} = 3y^2 + 4xy The only thing I could see working is a substitution, but I can't work out which one to use. I've tried letting v = xy, or v = y/x, but neither of those seem to produce anything useful. Can anyone give me a hint?

can someone help me solve the differential equation that takes the following form? y''+Ay'+By+Cy^2=f(x), y is function of x Thanks a lot!

Homework Statement Felix, a Red bull skydiver, (mass m) who drops out of a hovering helicopter, falls long enough without a parachute(so the drag force has strenght kv2 ) to reach his first terminal velocity ( denoted v1). When his parachute opens, the air resistance force has a strenght Kv...

Homework Statement A tank containing 400 liters of water has 10 kg of salt solute (dissolved salt). Some brine containing 0.03kg/L of salt is then introduced at a rate of 2 L/min. The solution is constantly mixed and evacuated at a rate of 2L/min, such that the volume remains constant. If...

Hello MHB, I wanted to post a challange question that is hopefully not really difficult, if the question is not understandable make sure to write it so I can try explain!:)Calculate the Differential equation for y''+2y'=0 that satisfy \lim_{x->\infty}y(x)=1 and y(0)=0 Regards, |\pi\rangle

Hi All, Please I need your assistance to solve this PDE below: \frac{\partial^2 X}{\partial t^2} - \frac{\partial^2 X}{\partial z^2} + a(z,t) \frac{\partial X}{\partial t} + b(z,t) \frac{\partial X}{\partial z} +c(z,t) X =\Phi(z,t) With initial and boundary condition...

Hello MHB, (x^2+1)y'-2xy=x^2+1 if y(1)=\frac{\pi}{2}What I have done: Divide evrything by x^2+1 and we got y'-\frac{2xy}{x^2+1}=1 we got the integer factor as e^{^-\int\frac{2x}{x^2+1}}= e^{-ln(x^2+1)} Now I get (e^{-ln(x^2+1)}y)'=e^{-ln(x^2+1)} and this lead me to something wrong, I am doing...

Homework Statement Solve the following differential equation by power series and also by an elementary method. Verify that the series solution is the power series expansion of your other solution. y'' = - 4y Homework Equations The Attempt at a Solution y'' = - 4y \\ \frac{d^{2}y}{dx^{2}}...

Hi I am trying to solve dy/dx = 3x^2-2x+2+(8/x *y) Can anyone show me how to rearrange to standard form as I am mightly confused :(

Homework Statement Find the general solution to the differential equation y'' -16y = 0, where y is a function of x. Give initial conditions that would give a unique solution to the eqution. For the differential equation y'' - k2y = R(x), with k ≠ 0 a real constant, show that it has a...

Hi! I would like to ask what is the general solution of the following differential equation \frac{\partial X_x}{\partial t} = - \frac{\partial X_t}{\partial x} Thank you very much. P.S. If you have some good resiource about this tyoe of equation to recommend please do so.

can anyone help me with MATLAB code for for solving a state homogeneous differential X=state vector Xdot(t)=AX(t)+BU(t) U is the control input i have the...

Find a solution to the following second order differential equation xy'+y=1/y^2 My Attempt: P= y'= dy/dx x dy/dx + y = 1/y^2 dy/dx + y/x = 1/xy^2 Integrating Factor = e^∫1/x dx = e^lnx y e^lnx=∫ (e^lnx)(1/xy^2) dx

Obtain the solution to the differential equation: \frac{dy}{dx} = \frac{1+y^2}{1+x^2} Multiple choice answer: a) \frac{Cx}{1-Cx} b) \frac{Cx}{1+Cx} c) \frac{C-x}{1-Cx} d) \frac{1-Cx}{x+C} e) \frac{x+C}{1-Cx} Tried integrating two sides to arrive at arctan y = arctan x + C, but not sure...

A differential equation of solitary wave oscillons is defined by, $$ \Delta S -S +S^3=0 $$ **How can we write this equation as,** \begin{equation} \langle(\vec{\nabla}S)^2\rangle+\langle S^2\rangle-\langle S^4\rangle=0 \tag{1} \end{equation} where $\langle f\rangle:=\int d^Dx f(x)$...

Hi folks! This one got me in doubts... Homework Statement Solve IVP (Initial Value Problem): (2xy+sin(x))dx+(x^{2}+1)dy=0, y(0)=2 Is the solution unique? Motivate why! Homework Equations Relevant equations for solving the exact equation... The Attempt at a Solution I can...

Given the following differential equation x*x''+(x')^2+y*y''+(y')^2=C where C is a constant and all differentiation is with respect to time Can i equal the first and second parts of the equation into different constants and solve separately?, meaning solving the system...

Solve the equation m\frac{d^{2}x}{dt^{2}} + c\frac{dx}{dt} + kx = (ax + b)^{2} + c^{2} for the constants m, c, k The right hand side a, b, and c are arbitrary digits. For me they are a = 2, b = 3, and c = 8. The problem recommends creating a linear system of equations for me to solve. This...

Homework Statement dy/dt = k*y*ln(y/M), where M and k are constants. Show that y = Meaekt satisfies the above equation for any constant a. Homework Equations y' = ky y = P0ekt The Attempt at a Solution Taking the derivative of y, I get: (Meaekt)*(aekt)*k which is, ky*aekt ..and I'm...

Hello! It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation: it's a non-linear second order differential equation. ay''+b|y|y'+cy+dx=0 Some ideas?

Find a particular solution for the following equation: y"+2y'+y=12.5e-t I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method: →y"+2y'+y=12.5e-t r2+2r+1=0 r=-1 *not even sure if this part is useful →yp=e-t yp'=-e-t yp"=e-t...

Homework Statement y''+y= H(3pi)(t) y(0)=1 y'(0)=0 H(3pi)(t) means the heaviside function such that it is 1 above 3pi and 0 otherwise. Homework Equations The Attempt at a Solution Taking the laplace of both sides, I have that: L(y) = (L(H(3pi)(t))+s) / (s^2 + 1)...

Hi everyone, :) Continuing from http://www.mathhelpboards.com/f17/method-reduction-order-variation-parameters-4574/ thread, my friend gave me another question. He wants to check his work specifically on parts a) and d). So I will only focus on those parts. Question Summary: Given the Riccati...

Homework Statement Find the general solution for the following differential equation: y'' + x(y')^2 = 0. Homework Equations Integration, differentiation... The Attempt at a Solution Usually for these sort of DE you could use the substitution v(x) = y'(x) and this would simplify...

Homework Statement The only singularities of the differential equation y''+p(x)y'+q(x)y=0 are regular singularities at x=1 of exponents \alpha and \alpha', and at x=-1 of exponents \beta and \beta', the point at infinity being an ordinary point. Prove that \beta=-\alpha and \beta'=-\alpha'...

Hello! I'm stuck at the moment with this differential equation. I've been trying to use the method for solving these equations, but my answer is not correct according to my book. Could anyone please explain what I'm doing wrong? Thanks!