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Particular Solution of a Differential Equation

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Question

Solve : $(e^{3} + 1) cos x d x + e^{y} sin x d y = 0$

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Solution

$(e^{3} + 1) c o s x d x = - e^{y} s i n x d y (e^{3} + 1) \int (\frac{c o s x}{s i n x} d x) = - \int e^{y} d y (e^{3} + 1) l o g | s i n x | = - e^{y} + c$

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