Question

(D²+3D+2)y=cos(2x)

Could you please solve this differential equation as

1. Successive Integration

2. Method of Parameter variation

3. Method of Undetermined coefficients

Just one way is also thankful!

hint:

Answer 1

We have found out the solution of the given Non Homogeneous differential equation with constant coefficients with the help of rhe Method of parameter Variation.

First, the complementary solution y​​​​​​c(x) is to be found out with the help of the characteristic equation of the associated Homogeneous differential equation.

Let y​​​​​​c​​​(x)= C​​​​​​​​1 y​​​​​​1 +C​​​​​​2 y​​​​​​2

The particular solution is given by y​​​​​​p(x)= u​​​​1 y​​​​​1 + u​​2 y2

The step by step explanatory solution is provided below