Question

Solve `(D^2+D)y=e^(4x)`  

Answer 1

For auxiliary equation, 

`D^2+D=0` 

Solving we get, 

`D=-1,0` 

∴` C.F.= C_1e^-x+C_2e^(o x)` 

∴ `C.F=c_1 e^-x+C_2` 

For P.I., 

`y= (e^(4x))/(D^2+D)` 

Now, put D = 4 

∴ `y= e^(4x)/(4^2+4)=e^(4x)/20` 

∴ The complete solution is,` y=C_1  e^-x+C_2+e^(4x)/20`