It's a nonhomogeneous linear equation. So you'll need to find a particular solution of the nonhomogeneous equation and the general solution of the related homogeneous equation

The homogeneous equation is

The characteristic equation is , which has roots of r=6 and r =1.

So the general solution of the homogeneous equation is

Now we need any particular solution of

will do

so the general solution on the nonhomongeneous equation is

Now we need to find the two coefficients by using the initial conditions.

Solving the two equations simultaneously, and

so our final solution is