Solving Inhomogeneous equation

[darkspym7]

Homework Statement

Solve the inhomogeneous equation y'' + 4y = 4 with y(0)=0 and y'(0)=0.

The Attempt at a Solution

let Y(t) = A, A being some constant
Y'(t) = 0
Y''(t) = 0

Y''(t)+4Y(t)=4
=> 4Y(t)=4
=> 4A=4
=> A=1
=> y(t)=1
But y(0)=0, so that cannot be correct.

Any tips?

 

[EnumaElish]

It looks like y is not a constant function; but a variable function that satisfies y'' + 4y = 4 with y(0)=0 and y'(0)=0.

 

[darkspym7]

It looks like y is not a constant function; but a variable function that satisfies y'' + 4y = 4 with y(0)=0 and y'(0)=0.

Yeah, I saw that, but how could I go about solving it if the right hand side is constant?

 

[Rainbow Child]

The function y(t)=1 is a particular solution. You have to add this to the general solution of the homogeneous equation. Can you find it?