In problem the indicated function y 1 (x) is a solution of the associated homogeneous equation Use the method of reduction of order to find a second solution y 2 (x) of the homogeneous equation and a particular solution y p (x) of the given nonhomogeneous equation y ' ' 3y ' 2y 5e 3x y 1 e x ...

Define y uxe x so y ue x ue x y ue x 2ue x ue x and y 3y 2y e x u e x u 5e 3x If w ...

In problem the indicated function y 1 (x) is a solution of the associated homogeneous equation. Use

Question:

In problem the indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of‑ reduction of order to find a second solution y₂(x) of the homogeneous equation and a particular solution y_p(x) of the given nonhomogeneous equation.

y'' ‑ 3y' + 2y = 5e^3x; y₁ = e^x