linear differential equation

For the Ordinary Differential Equation $\frac{d^2x}{dt^2} - 5\frac{dx}{dt} + 6x = 0$, with initial conditions $x(0) = 0$ and $\frac{dx}{dt}(0) = 10$, the solution is

Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$