First, find the complementary solution by setting the left side equal to 0.
y``-5y`-6y=0 <- homogeneous solution, so,
λ^2 - 5λ -6 =0
Solve λ
\[y_c = c_1e^{\lambda _1 x} + c_2e^{\lambda _2 x}\]
Then, find out the particular solution, try \(y_p = Asinx+Bcosx\) (No guarantee that it works though). Differentiate it and solve the A and B. Then, you get \(y_p\)
\[y = y_c +y_p\]
@Aperogalics I never intend to give out the answer..