Use the method of undetermined coefficients to find one solu

Use the method of undetermined coefficients to find one solution of y8y+20y=8e^5t.

Solution

We can guess the form of one solution based on the inhomogeneous componet ie 8e^{5t}

The guess is :yp=A e^{5t}

Substituting gives

25Ae^{5t}-40 Ae^{5t}+20Ae^{5t}=8e^{5t}

5Ae^{5t}=8e^{5t}

Giving :A=8/5

So one solution is

yp= 8/5 e^{5t}