# Thread: maximum value for initial value problem?

1. ## maximum value for initial value problem?

Let y be the solution of the initial value problem
y" + y = -sin(2x) where y(0) = 0 and y'(0) = 0
The maximum value of y is___?

I can find the general solution to this diff EQ.... but I don't know how to answer their question.

Thanks =)

2. Originally Posted by plopony
Let y be the solution of the initial value problem
y" + y = -sin(2x) where y(0) = 0 and y'(0) = 0
The maximum value of y is___?

I can find the general solution to this diff EQ.... but I don't know how to answer their question.

Thanks =)
If you have found $y$, differentiate it to find $y'$, set it equal to $0$ and solve for $x$.

Then use the second derivative test to determine that it is in fact a maximum.