9. differential equations — ગણિત ધોરણ 12 સાયન્સ — Question

$\frac{{dy}}{{dx}}(\tan y) = 2\sin x\cos y$ ==> $\frac{{\sin y}}{{{{\cos }^2}y}}dy = 2\sin xdx$

==> $\int {\frac{{\sin y}}{{{{\cos }^2}y}}} dy = 2\int {\sin xdx} $ ==> $\frac{1}{{\cos y}} = - 2\cos x + c$

$\therefore $ $\sec y + 2\cos x = c$.