Differential Equations

Question

Would someone explain these to the very end of the problem? I'm still a bit confused.

 

Let y be the solution of the initial value problem.
y″+y=−sin(2x)
y(0)=0,y′(0)=0.

The maximum value of y is = ?

2. Consider the initial value problem
y′′+4y=e^(−t)
y(0)=y0, y′(0)=y′0

Suppose we know that y(t)→0 as t→∞. Determine the solution and the initial conditions.

y(t)= ?
y(0)= ?
y′(0)= ?

Answer 1

https://www.wyzant.com/resources/answers/294959/differential_equations