<s>[INST] Solution of differential equation in Trigonometric functions of $x$ and $y$ If $$\frac{dy}{dx} +\frac{\cos x(3\cos y-7\sin x-3)}{\sin y(3\sin x-7\cos y+7)}=0$$
Attempt: $(3\sin x\sin y-7\cos y \sin y+7\sin y)dy+(3\cos x\cos y-7\sin x\cos -3\cos x)dx =0$
could some help me how to solve it , thanks
 [/INST] Hint: $$\dfrac{\sin y}{\cos x}\dfrac{dy}{dx}=-\dfrac{d(\cos y)}{d(\sin x)}=-\dfrac{3\cos y-7\sin x-3}{3\sin x-7\cos y+7}$$ Now use a suitable variable transformation to get a familiar equation as in example 4.14.
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