Basic differential equation problem

[sunnyandzorro]

Verify that every member of the family of functions y = A sin(5/2t) + B cos(5/2t) is a solution to 4y" = -25y

I attached my crappy work so you can see where I am getting stuck... what am I getting wrong?

Thanks

 

[Deleted member 4993]

Verify that every member of the family of functions y = A sin(5/2t) + B cos(5/2t) is a solution to 4y" = -25y

I attached my crappy work so you can see where I am getting stuck... what am I getting wrong?

Thanks

y' = A(5/2)cos(5t/2) - B(5/2)sin(5t/2)

y" = -A(25/4)sin(5t/2) - A(25/4)cos(5t/2)

 

[sunnyandzorro]

Thanks, I knew it was something silly!