JO SUUS. 7.12. Solve the BVP y" = -2e-3y + 4(1+x)-3, 0<x<1, subject to y(0) = 0, y' (O) = 1, y(1) = In 2. Compare to the exact solution, y(x) = ln(1+x).
Solve the given homogeneous Cauchy-Euler differential equations (a) (d) ry" + y = 0 zy' - 3.cy – 2y = 0 ry" – 3y = 0 z?y" + 3xy – 4y = 0 z’y' + 5xy' + 3y = 0
Question 2 > Solve y' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude O Oscillating with increasing amplitude
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude o Oscillating with increasing amplitude
1) Solve the following ODE with IVP 2y" + 6y' - 8y = 0 y(0) = 4 y'(0) = -1
Solve the differential equation below using series methods. y' + 3xy' + 8y = 0, y(0) -1, y'(0) = – 5 Find the first few terms of the solution y(x) = axxk. k=0 ao = Preview ai Preview A2 = Preview = a3 = Preview 24 = Preview 05 = Preview
Solve without using laplace 1. 3y" – 8y' – 3y=0 y(0)=10, y'(0)=0
4. (10 points) Solve the given IVP: y'"' + 8y" +22y' + 20y = 0; y(0) = 0, y'(0) = 1, y" (0) = 2.
Problem 3 Solve the initial value problems using Laplace Transforms (a) y' + 8y = t2 y(0) = -1 (b) y" – 2y' – 3y = e4t y(0) = 1, y'(0) = -1
Using Integration Factor method to solve
General
b) Find Green's function for the BVP y(4) = -f, 0<x< 1, y(0) = y'(0) = y(1) = y'(1) = 0. u(n) = axu(k-1) +g(t) k=1 lo U(t) = U(0)U1(t) +Ư (0)U2(t) + ... +Un-1)(0)Un(t) +| Unt – TÌq(T)dx U (0) = 0 U (0) = 0 Tkk-2)(0) = 0 vlk-1)(0) = 1 - (0) = 0 Un-1)(0) = 0