Find the solution of y'' + 25y = 150cos(5t)
I have found the the complimentary function to be y= Acos(5t) + Bsin(5t)
When I worked out the particular integral I came as far as this:
t(-25C cos(5t) - 25Dsin(5t)) - 10Csin(5t) + 10Dcos(5t) + 25t(Ccos(5t) + Dsin(5t)) = 150 cos (5t)
What i dont unerstand is why the above simpifies to 150cos(5t)??
Thank you for any help.