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2. (20 pts) Solve the following ODE: 3. (30 pts) Solve the following (ODE. y"2y'2y = 2x
1. a) Solve the following linear ODE. dy * dx + 2y = 4x2, x > 0 b) Solve the following ODE using the substitution, u = dy (x - y) dx = y c) Solve the Bernoulli's ODE dy 1 + -y = dx = xy2 ; x > 0
2. (30 pts) Use the method of undetermined coefficients to solve the following ODE y"5y6y -12 e-2=, y(0) = 0, y'(0) = -3
4. (25 points) Solve the following ODE using classical 4th-order Runge- Kutta method within the domain of x = 0 to x= 2 with step size h = 1: dy 3 dr=y+ 6x3 dx The initial condition is y(0) = 1. If the analytical solution of the ODE is y = 21.97x - 5.15; calculate the error between true solution and numerical solution at y(1) and y(2).
(8a) Solve the ODE y" - 3y' = 4y (86) Solve the ODE y" - 3y' = 4y + 3 (9a) Solve the ODE" = - 4y (9b) Solve the ODE y" = -4y - 8x
Problem 1 of 5 (20 points) Solve the following ODE by the method of variation of undetermined coefficients
y21.6y + 1.2yz + 4.8 ed 8. (30 pts.) Take home the following problem, solve it and hand it out till May 8. Write the ODE y -4y' y3 0 as a system, solve it for y2 as a function of y1 and graph some of the trajectories in the phase plane. (refer page 186 of the textbook)
y21.6y + 1.2yz + 4.8 ed 8. (30 pts.) Take home the following problem, solve it and hand it out till May...
1) Solve the following ODE with IVP 2y" + 6y' - 8y = 0 y(0) = 4 y'(0) = -1
1) (40 pts total) Solving and order ODE using Laplace Transforms: Consider a series RLC circuit with resistor R, inductor L, and a capacitor C in series. The same current i(t) flows through R, L, and C. The voltage source v(t) is removed at t=0, but current continues to flow through the circuit for some time. We wish to find the natural response of this series RLC circuit, and find an equation for i(t). Using KVL and differentiating the equation...
Solve the following ODE. Enter the constants as C1. C2. and C3.