# The general solution of $e^x\cos y\;dx-e^x\sin y\;dy=0$ is:\begin{array}{1 1}(A)\;e^x\cos y=c & (B)\;e^x\sin y=c\\(C)\;e^x=c\;\cos y & (D)\;e^x=c\;\sin y\end{array}

Toolbox:
• If a linear differential equation is of the form $\large \frac{dy}{dx}$$=f(x) then it can be solved by seperating the variables and then integrating Given e^x \cos y \;dx-e^x \sin y\; dy=0 Dividing by e^x we get \cos y \;dx=\sin y \; dy =>\large\frac{\sin y}{\cos y}$$dy=dx$
(ie)$\tan y \;dy=dx$
Integrating on both sides we get,
$\int \tan y \;dy=\int dx$
$=> -\log_e |\cos y|=x+c$