What is the solution for the second order differential equation $\frac{\mathrm{d} ^{2}y}{\mathrm{d} x}^{2}+y=0$, with the initial conditions $y\left | _{x-0}=5\:and\:\frac{\mathrm{d} y}{\mathrm{d} x}\right |_{x-0}=10$?

1. $y=5+10\sin x$
2. $y=5\cos x-5\sin x$
3. $y=5\cos x+10 x$
4. $y=5\cos x+10 \sin x$