I am having problems with this ODE:

Derive the solution of the ordinary differential equation

$\displaystyle \frac{d^2y}{dx^2} = f(x)$

$\displaystyle x > 0 , y(0) = 0 $

$\displaystyle \frac {dy}{dx} (0) = 0 $

In the form:

$\displaystyle y(x) = \int_{0}^{x} (x-t)f(t)dt $

Can't use particular integral/complementry function... I have tried to use a laplace transform but get stuck on integgrating an unknown function $\displaystyle f(x)$... also dont understand the change of variable to 't' - the $\displaystyle (x-t)$ suggests to me a laplacian shift. I am stuck... Thanks for looking!