# ode

1. ### First order separable Equation ODE

1. Homework Statement \frac{dy}{dx}\:+\:ycosx\:=\:5cosx I get two solutions for y however only one of them is correct according to my online homework (see attempt at solution) 2. Homework Equations y(0) = 7 is initial condition 3. The Attempt at a Solution \int \:\frac{1}{5-y}dy\:=\:\int...
2. ### I Linearly-damped rotational motion

http://imgur.com/a/8QjoW http://imgur.com/a/8QjoW Hello- I am trying to determine the dynamics of this linearly-damped hinge. Assuming that: v(0) = 0 damping constant = b door has mass = m I was able to determine that: ∑Fx = -Fd * cos(45-θ/2) + Rx = m*dvx/dt ΣFy = -Fd * sin(45-θ/2) - Fg +...
3. ### I Linearizing a System of ODE's

I am given the equations of Lorenz with respect to deterministic non-periodic flow: \frac{dX}{dt} = Pr(Y-X), X(0)=X_{0} \frac{dY}{dt} = -XZ + rX - Y, Y(0) = Y_{0} \frac{dZ}{dt} = XY-bZ, Z(0) = Z_{0} where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...
4. ### How to find r(t) when we are given conditions - ODE

1. Homework Statement Consider the following problems In #2, they start the solution by saying: r(t)=u(t-1) in #3, they start by saying that r(t)=t-tu(t-1) I understand how to solve the problem once you get r(t), I just don't understand how they decide what r(t) is going to be.
5. ### Second order non homogeneous ODE, IVP

1. Homework Statement I need to solve: x^2y''-4xy'+6y=x^3, x>0, y(1)=3, y'(1)=9 2. Homework Equations 3. The Attempt at a Solution I know that the answer is: y=x^2+2x^3+x^3lnx Where did I go wrong. I was wondering if it's even logical to solve it as an Euler Cauchy and then use variation...
6. ### 2nd Order Linear ODE-Derivation of system-issue

1. Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. 2. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 3. The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but...
7. ### Rewriting ODE's into lower orders

1. Homework Statement Express \frac{d^{2}x}{dt^{2}} + \sin(x) = 0 In a system in terms of x' and y'. 2. Homework Equations 3. The Attempt at a Solution I seen this example: x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2} Where they then wrote...
8. ### I Constant solution and uniqueness of separable differential eq

Hi, I am learning ODE and I have some problems that confuse me. In the textbook I am reading, it explains that if we have a separable ODE: $x'=h(t)g(x(t))$ then $x=k$ is the only constant solution iff $x$ is a root of $g$. Moreover, it says "all other non-constant solutions are separated...
9. ### Obtaining General Solution of ODE

1. Homework Statement So they want me to obtain the general solution for this ODE. 2. Homework Equations I have managed to turn it into d^2y/dx^2=(y/x)^2. 3. The Attempt at a Solution My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the...
10. ### Solve for the solution of the differential equation

1. Homework Statement Solve for the solution of the differential equation and use the method of variation of parameters. x - x = (e^t) + t 2. Homework Equations W= (y2y1)-(y2y1) v1 = integral of ( g(t) (y1) ) / W v2 = integral of ( g(t) (y2) ) / W 3. The Attempt at a Solution yc= c1...
11. ### A Initial value ODE with shifting forcing function

Use laplace Transform to solve this ode: So I got: sV(s)-V(0)-12V(s)=U(s+5) V(s)(s-12)=U(s+5)+1 V(s)=[U(s+5)+1]/(s-12) Now to go back to time domain with Inverse Laplace Transform...My question is, how to transform U(s+5)/(s-12)? Any help? Thanks guys
12. ### Solving a System of ODE for Steady State

I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...
13. ### A non-exact nonlinear first ODE to solve

1. Homework Statement Solve the following equation. 2. Homework Equations ( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0 3. The Attempt at a Solution M = ( 3xy4 + 2xy ) N = ( 2x3y3 - x2 ) ∂M/∂y = 12x2y3 + 2x ∂N/∂x = 6x2y3 - 2x Then this equation looks like that the integrating factor is...
14. ### I An application of free fall (DE) model to industry

Could someone tell me an application of the model of free fall to industry or more generally by using newton's second law and the law of gravitation, construct a model similar to the free fall one, that has an application in industry
15. ### Abel's Equation and Wronskian for find out y2

1. Homework Statement x²y''+xy'+(x²-0,25)y=0 y1= x^-1/2*sin x 2. Homework Equations Abel's equation: W= c.e^-(integrate (p(t)) 3. The Attempt at a Solution My Wronskian gave me a first order ODE that I really don't know solve. x^-1/2*sinx y' + (1/2 x^-3/2 sin x- x^-1/2cosx) y2 I don't...
16. ### What conditions are needed to get a stable limit cycle here?

1. Homework Statement I want to find conditions over A,B,C,D to observe a stable limit cycle in the following system: \frac{dx}{dt} = x \; (A-B y) \hspace{1cm} \frac{dy}{dt} = -y \; (C-D x) 2. Homework Equations Setting dx/dt=0 and dy/dt=0 you can find that (C/D , A/B) is a fixpoint. 3...
17. ### 4th order Runge Kutta Matlab with 2 2nd order ode

1. Homework Statement Hi There! MX''=Fn(sin θ - uCos θ ) MZ''=Fn(cos θ + uSin θ ) - Mg Fn,M,θ,u is constant fn/M = 0.866 M = 6000 θ = 30 u = 0.5774 i split my motion equation into 2 individual 1st ode, X' = Vx Z' = Vz Vx'=[fn*(sin θ - uCos θ )]/M Vz'={[fn(cos θ + uSin θ )]/M} - g...
18. ### 2nd order differential equation (nonhomogenous)

1. Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? 2. Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. 3. The Attempt at...
19. ### Inhomogeneous 2nd ODE

If i have 3y" - 2y' -y = 14 + e2x+8x And i want to find the general solution. Obviously first i obtain the characteristic eqn, yc, by making it into a homogeneous eqn. Then i can get yp BUT Am i able to get yp for the e2x and the 14 + 8x separately, then add them together for yp? Thanks
20. ### Series solution of ODE near singular points with trig

1. Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...
21. ### System of ODEs with RK4 & step doubling in Fortran : damping

Hello, I'm recently trying to code a solver for a system of differential equations u'(t) = F(t,u), using a Runge Kutta 4 method with an adaptative stepsize. For this, I'm using the 'step doubling' method, which is the following : suppose that we now the solution u(i) at time t(i). Then, the...
22. ### Solve a 2nd order Ordinary Differential Equation

1. Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e 2. Homework Equations No clue how to start this 3. The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0
23. ### Find the approximate linear ODE system

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!
24. ### Heun's method question

Hi there, in my notes for Heun's method for solving an ODE, I have y(new) = y(old) + 0.5(k1 + k2)Δh And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1 So if for example I have a simple differential equation like du/dt = au It would be du/dt = 0.5(k1 + k2) du/dt...
25. ### Matrix-free iteration methods and implicit ODE solvers

Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...
26. ### Construct a second order ODE given the solutions?

1. Homework Statement I've been stuck on this problem for three days now, and I have no clue how to solve it. Construct a linear differential equation of order 2, for which { y_1(x) = sin(x), y_2(x) = xsin(x)} is a set of fundamental solutions on I = (0,\pi) . 2. Homework Equations...
27. ### ODE RC Circuit Problem

1. Homework Statement Suppose an RC series circuit has a variable resistor. If the resistance at time t is given by by R = a + bt, where a and b are known positive constants then the charge q(t) on the capacitor satisfies (a+bt) q' + (1/C)q = V where V is some constant. Also q(0) = q_0 Find...
28. ### Zero-Input/Zero-State Response vs. Homogenous/Particular Solution

I have a question regarding the solutions to linear-ordinary differential equations. I had originally learned that the solutions to such differential equations consist of a homogenous solution and particular solution. The homogenous response is due to initial conditions while the particular...
29. ### Trapping region for a nonlinear ODE system

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or wich code in Mathematica o Matlab could help me to find the optimal trapping region.
30. ### Intro Math Mastering Differential Equations

During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like); Ordinary...