Find the solution of y''+3y'-4y=36e^2t with y(0)=5 and y'(0)=4. Find y(t). I don't know where to start, but I just need the answer.
This is just a linear DE with constant coefficients. You must have started studying them, or you would not have gotten this problem.
you have (D+4)(D-1)y = 0 for the homogeneous equation.
y = c1 e^(-4t) + c2 e^t + 6e^(2t)
Now use your two points to find c1 and c2