I have tried with some methods but cannot proceed the following system of differential equations:
$$\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}v_1(t)=-v_1(t) \cos(t)\sin(t)+v_2(t) \sin^2(t)\\ \displaystyle \frac{\mathrm{d}}{\mathrm{d}t} v_2(t)=-v_1(t) \cos^2(t)+v_2(t) \cos(t)\sin(t)$$
Can someone help me what method to use to solve this system of equations. Thank you.