Answer:
Step-by-step explanation:
[tex]y''-4y=cosx[/tex]
The auxialary equation and solutions are as follows:
[tex]m^2-4=0\\m=2,-2[/tex]
General solution is
[tex]y=Ae^{2x} +Be^{-2x}[/tex]
Right side =cosx
Particular Integral
= [tex]\frac{cosx}{-1-4} =\frac{-cosx}{5}[/tex]
Hence full solution is
