Homogeneous differential equations of second order I can not find other solutions of the equation
$$
y'' + 4y = 0
$$
addition of the solutions $y = 0$ and $y = \sin 2x$. There are positive solutions? Or solutions in terms of exponential function? Thanks.

The characteristic equation is 
$$r^2+4=0$$
so its roots are $r_1=2i$ and $r_2=-2i$ and then the general solution is 
$$y(x)=A\cos(2x)+B\sin(2x)$$
