3. Solve y" + 2ay' +y -sin(t) with initial condition y(0) -y'(0)0 for all values of a 2 0. Plot t...
(Matlab) Use Matlab's built-in Runge-Kutta function ode45 to solve the problem 1010y -xz +28x - y 3 on the interval t є [0, 100 with initial condition (z(0), y(0),z(0)) = (1,1,25), and plot the trajectory of the solution ((t), (t)) forte [0, 100 (Matlab) Use Matlab's built-in Runge-Kutta function ode45 to solve the problem 1010y -xz +28x - y 3 on the interval t є [0, 100 with initial condition (z(0), y(0),z(0)) = (1,1,25), and plot the trajectory of the...
2. Indicate a rectangle (that is, an interval of t-values and an interval of y-values) in which the requirements of the theorem on existence and uniqueness are satisfied for the non-linear initial value problem dy 1 sin(t)y(ty 2y +4t - 8) = 0 dt with the given initial condition. If no such rectangle exists, explain why not. Do NOT solve the equation y(5) 5 (b) (c) y(1)4 (a) y(0) 3 = = 2. Indicate a rectangle (that is, an interval...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition: For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
1. Find the particular solution of the differential equation dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x) satisfying the initial condition y(0)=4y(0)=4. 2. Solve the following initial value problem: 8dydt+y=32t8dydt+y=32t with y(0)=6.y(0)=6. (1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
use laplace transform to solve initial value problem. thank you y(0) = 0 y(0) = 1, 11. y" + 4I/ + İSy = δ(t-n) + δ(t-37), r + -2(t-r) sin 3 (t- y(0) = 0 y(0) = 1, 11. y" + 4I/ + İSy = δ(t-n) + δ(t-37), r + -2(t-r) sin 3 (t-
Solve using Matlab Use the forward Euler method, Vi+,-Vi+(4+1-tinti ,Vi) for i= 0,1,2, , taking yo y(to) to be the initial condition, to approximate the solution at t-2 of the IVP y'=y-t2 + 1, 0-t-2, y(0) = 0.5. Use N = 2k, k = 1, 2, , 20 equispaced time steps (so to = 0 and tN-1 = 2). Make a convergence plot, computing the error by comparing with the exact solution, y: t1)2 -exp(t)/2, and plotting the error as...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
(1 point) Solve the following ODE subject to the initial condition y(0) = 3: V = 1² - 6² x² – 6² Also, calculate y(1/2). y = y(1/2) =