Differential equation Definition and 1000 Threads

Homework Statement Inside the earth, the force of gravity is proportional to the distance from the center. If a hole is drilled through the Earth from pole to pole and a rock is dropped in the hole, with what velocity will it reach the center? The Attempt at a Solution I think that the...

Homework Statement If d^2s/dt^2 = a, given that ds/dt = u and s = 0, when t = 0, where a, u are constants show that s = ut + .5at^2 2. The attempt at a solution du/dt = a cross multiplying and then integrating and we get u = at ds/dt = at cross multiply and...

I have to solve the differential equation y''+(1-t) y' + y= sin(2t) can someone judge this? How could I continue it? y=\sum_{n=0}^{∞}{a_{n} t^{n}} y'=\sum_{n=1}^{∞}{a_{n} n t^{n-1}} y''=\sum_{n=2}^{∞}{a_{n} n(n-1) t^{n-2}} sin(2t)=\sum_{n=0}^{∞}{\frac{2^{2n}}{2n!} t^{2n}} y''+(1-t) y'...

Friends I have one doubt Below given equation is linear or non linear :)

EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...

Task 7 Show that y=(1/4)tsin2t satisfies equation d2y/dt2+4y=cos2t Find the general solution and deduce the solution which satisfies y(0)=0 and y'(0)=0. What happens as t increases? Solution In the end I stay with: y=Acos2t+Bsin2t+(1/4)tsin2t...

y"+2y'+y=2e^-t I tried to find the solution for this nonhomogenous diff. Equation but i could not. First i took a function Y(t)=Ae^-t but i was getting 0=2e^-t. To get rid of that i took another y'+y=2e^-t and found the solution y=2te^-t + ce^-t. Noticed that first part of this finding is...

Homework Statement Find the maximal ground reaction force for the limiting case where the speed at initial contact is equal 0 (Vo=0) expressing it as a mulitple of the body weight (mg) ω = √k/m Homework Equations Y1(t) = A sinωt + B cos ωt + g/ω^2 The Attempt at a Solution I...

Here is the DE: Δu(r,θ)=0, 1 ≤ r ≤ 2, 0 ≤ θ ≤ pi and here are the Boundary Conditions: u(1,θ)=sin(θ), u(2,θ)=0, u(r,0)=0, u(r,pi)=0 Based on the Boundary Conditions I believe this is half of an annulus. Using the 2D Laplace equation for polar coordinates, find the solution u(r,θ). I've...

Find the Fourier series solution to the differential equation x"+x=t It's given that x(0)=x(1)=0 So, I'm trying to find a Fourier serie to x(t) and f(t)=t, and I'm know it must a serie of sin... So here's my question...the limits of integration to the Bn, how do I define them? Will...

Homework Statement Hi, Just wondering if anyone knows how to solve the following as I am not sure where to start at all: y''' + 8y = xsin(2x) Any help would be great. Homework Equations The Attempt at a Solution I'm thinking solving the homogeneous DE y'''+8y = 0 and...

Homework Statement Given y_1=x is a solution, solve the differential equation Homework Equations y''+xy'-y=0 The Attempt at a Solution Since I am given y_1=x (is there a hotkey for adding TeX tags so I don't have to manually type these tags over and over? So tedious.) then I...

Homework Statement A bullet of mass m strikes an amor plate with initial velocity v0. As the bullet burrows into the plate, its motion is impeded by a frictional force which is directly proportional to the bullet's velocity. There are no other forces acting on the bullet. -Use Newton's Second...

What is the answer of this differential equation. ((d^2) r)/((ds)^2) +(m/(r^2)) -(nr/3)=0 the boundary conditions (i) r=a when s=0 and (ii) dr/ds =0 when r=b. m and n are constants.

Consider the first order differential equation dy/dy = f(t,y) = -16 t^3 y^2 with initial condition y(0)=1 Using second order Adams-Bashforth method, write a Fortran programming to generate an approximate solution to the problem. please forgive me for not trying because I really...

I have a problem that starts with the equation: r\frac{d^2u}{dr^2} + \frac{du}{dr} = 0 The solution I'm looking at says to do a substitution, letting u = r^m, which after differentiation and simplification results in: m^2 = 0 Up until this point, I understand (well, actually I don't...

Homework Statement Let ##y_1(x)= e^x## and ##y_2=x^2+1+e^x## solve the differential equation ##y^{'}+b(x)y=c(x)##. Find the overall solution of this differential equation. Homework Equations The Attempt at a Solution The overall solution => ##y=y_H+y_P## I don't know the english expression...

Mod note: Reinstated problem after poster deleted it. [/color] Homework Statement Just wondering if I did this correctly: ##y''+4y'+4y=e^{x}## and initial conditions ##y(0)=0; y'(0)=1## Homework Equations The Attempt at a Solution So I found the characteristic equation to be...

Homework Statement 1st problem - is this correctly done? \frac{dy}{dx} = (##x^2## - 1) ##y^2## , y(0) = 1 2nd problem - I really need help with this one. xy' - y = ##3x^2## , y(1) = 1 The Attempt at a Solution 1st problem: \frac{dy}{dx} = (##x^2## - 1) ##y^2## , y(0) = 1...

Homework Statement "Solve differential equation y''+y=2*cos x. Draw circuit of the equation and think about the strange behavior of the current." The attempt at a solution I was able to solve the equation, but I have no idea how to draw circuit about it, we haven't gone through this...

I have the following differential equation which I want to solve for y as a function of x \frac{dy}{dx}=\frac{C_{1}\left(C_{5}y+C_{6}\right)^{2}}{C_{2}\left(C_{3}y+C_{4}\right)-C_{7}\left(C_{5}y+C_{6}\right)^{6}} where C_{1},C_{2},C_{3},C_{4},C_{5},C_{6},C_{7} are constants. Can anyone...

Homework Statement A boy is on a boat, at a distance H from the shore, when he sees a girl (at the point on the shore where the distance is measured) running with a constant velocity u parallel to the shore. At that time, he moves towards her, with a speed v, in such a way, that the point of...

hello! I am facing some difficulties at the following exercise. "show that g(x)=x \cdot F(x) , where F(x)=\int_{0}^{x} {s(x)}dt , s(x)=\frac{sin(x)}{x} , satisfies the diffential equation xy'(x)-y(x)=xsin(x) , x ε R, and find all the solutions in this space. Show that the differential...

Homework Statement . Solve the differential equation: ##(3x^2-y^2)dy-2xydx=0##. The attempt at a solution. I thought this was an exact differential equation. If I call ##M(x,y)=-2xy## and ##N(x,y)=3x^2-y^2##, then the ODE is an exact differential equation if and only if ##\frac{\partial...

Hello - I asked a similar question before, but it was not resolved for me, and the person who answered was rude, so I did not continue the conversation. I read this here: http://tutorial.math.lamar.edu/Classes/DE/SecondOrderConcepts.aspx "If y_1(t) and y_2(t)are two solutions to a...

Homework Statement Solve x^{2}\times y'' - 4 \times x \times y' + 6 \times y = 0 for y(x) by first using the substitution v = ln(x) to obtain an equation involving y, dy/dv, d^2y/dv^2 and no x. Solve for y(v), then return to y(x). Homework Equations NA The Attempt at a Solution I know how...

Is there some systematic procedure to solve delay differential equation ? Here's one equation that I would like to solve \large \frac{1}{ \omega } \frac{dV_0(t)}{dt} = V_i(t) - \frac{V_o(t-T_d)}{k} where Td is the delay Thanks

Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...

I have had this question on my mind for a long time When we solve a differential equation like this \frac{dT}{dx}=0 Do we do this ? \int\frac{dT}{dx}dx=\int0dx\int dT=\int0dxT =c_1 Because if we were to separate variables this doesn't work, we're just integrating both sides in respect...

Hi, i have to reduce the order of a 2nd order differential equation, to solve it with a numerical method. The equation is: \ddot{r}+a\dot{r}+\frac{b}{r^{2}}=0 with a,b\geq0 I tried to reduce it substituting \dot{r}=v, but i don't know what to do with the term \frac{b}{r^{2}} ...

I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation? I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I...

Hello everyone, I'm having trouble understanding the solutions to DE's of the form: ay''+by'+cy=f(t) We've gone over them in class, I've talked with my friends, and it just doesn't make any sense to me. I was wondering if anyone on here would help me understand the solutions, it would be...

Solving differential with a step impulse. Hi, I have problem I know I should be able to do but I've been stuck on it for a while. Just looking to be pointed in the right direction. (dq^2/d^2t) + 2*ζ*ω*dq/dt + (ω^2)*q = u(t)/L Where u(t) is a step impulse, q is the charge through an...

Hi MHB. I'm having yet another doubt regarding differential equations. Can someone please help me out? Thanks. Consider the following differential equation: $${y}''+{y}'= x^{2}$$ I have found the homogeneous solution to be: $$y_{H}=c_{1} + c_{2}e^{-x}$$ But when finding the particular...

Homework Statement A car starts from rest.When it is at a distance s from its starting point,its speed is v and it acceleration is a = (25v + v^3). Show that dv = (25 + v^2)ds and find its speed when s = 0.01 2. The attempt at a solution a = v(dv/ds) = (25v + v^3) divide both sides by v...

Homework Statement Okay, I am trying to solve this Anharmonic Oscillator equation. Now I am given with the potential U=(1/2)x^2-(1/4)x^4 and Kinetic energy T=(1/2)x' ^2 So the Lagrangian becomes \mathcal L=T-U Now I have taken all the k's and m to be 1 Homework Equations...

Hi MHB. Can someone help me with this one please? I don't understand what the question is really saying...in particular part (c). I tried to set up dD/dt = k - D^1/2 but it doesn't seem correct. Thanks.

Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next. Consider dx/dt = x^3 - 4x Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t). Thanks!

Homework Statement Solve d^2x/dt^2 = (3x^3)/2 when dx/dt = -8 and x = 4 when t = 0 2. The attempt at a solution v = dx/dt dv/dx = d^2/dx^2 d^2x/dt^2 = v(dv/dx) = (3x^3)/2 v dv = (3x^3)/2 dx integrating and using limits and you get : v^2/2 -32 = (3x^4)/8 - 96 ...

I need to solve the following system of equations for n=0,1,2 subject to the given initial and boundary conditions. Is it possible to solve the system numerically. If yes, please give me some idea which scheme I should use for better accuracy and how should I proceed. The coupled boundary...

For polar coordinates, ##u(x,y)=u(r,\theta)##. Using Chain Rule: \frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta}\frac{\partial \theta}{\partial x} The book gave \frac{\partial ^2 u}{\partial x^2}=\frac{\partial...

Homework Statement using the method of separation of variables, solve ∂u/∂x=4∂u/∂y, where u=3e^-y - e^-5y when x=0. Homework Equations The Attempt at a Solution let u(x,y)=X(x)Y(y) =XY.

Homework Statement Solve (d^2x)/(dt^2) = 2x(9 + x^2) given that dx/dt = 9 when x = 0 and x = 3 when t = 0 Homework Equations The Attempt at a Solution v = dx/dt ...... dv/dx = d^2x/dt^2 dv/dx = v(dv/dx) v(dv/dx) = 18x +2x^3 integrating and evaluating using...

Hi, I'm somewhat new here, only posted a few times, and would like some help from you guys here if possible I'm stuck with a problem on the topic mentioned. x'=Ax A is a 2*2 matrix A = [-5 1] [-1 -3] Now I managed to find the eigenvalues which is -4, repeated twice (multiplicity 2) And the...

Hi, The definition (see attachment) says that f(x) is a solution to the differential equation if it satisfies the equation for every x in the interval. Assuming that I have a differential equation that I want to solve and the D.E. has an interval I_1, and I've come up a solution with...

Homework Statement Right so I had a standard systems of diff eqs involving repeated eigenvalues. When I find the last vector I have the equation \begin{pmatrix} 1 & 1\\ -1 & -1 \end{pmatrix} \begin{pmatrix} u_1\\ u_1 \end{pmatrix} = \begin{pmatrix} 1\\ -1 \end{pmatrix}The Attempt at a...

\sqrt{1-y^2}dx - \sqrt{1-x^2}dy=0, y(0)=\frac{\sqrt{3}}{2} rewriting the equation gives \frac{1}{\sqrt{1-x^2}}dx = \frac{1}{\sqrt{1-y^2}}dy Isn't this the integral for \sin^{-1}(x) & \sin^{-1}(y)? The back of book has y=1/2x+\frac{\sqrt{3}}{2}\sqrt{1-x^2}

Homework Statement Find the general solution: y'' - y' - 2y = -2t + 4t^2 Homework Equations The Attempt at a Solution r_1 = 2, r_2 = (-1) Set Y(t) = At^2 + B^t + C Y' = 2At + B Y'' = 2A 2A - 2At + B - 2At^2 + Bt + C = -2t + 4t^2 -2At^2 + (B-2A)t + 2A + B + C = -2t...

Solve the given differential equation by separation of variables $$y\ln{x}\frac{dx}{dy}=(\frac{y+1}{x})^2$$ I got it down to \ln{x}x^3-\frac{x^3}{3}=y^3+3y+y^2 At this point I had no idea how to solve having y^3 y^2 and y terms so I did what any good student would do and checked the back of...

Hello MHB, Solve the following system of linear differential equation $$f'=f-g$$ $$g'=f+g$$ with bounded limit $$f(0)=0$$, $$g(0)=1$$ could anyone check if My answer is correct? Just to make sure I understand correctly! ps we get $$\lambda=1-i$$ and $$\lambda=1+i$$ Regards, $$|\pi\rangle$$