Question

find the integration of equation e∧x+y∧x

Answer 1

$e^x+y^x=e^x+e^{log y^x}=e^x+e^{xlog(y)}$
take
$y=e^x+e^{xlog(y)}$
diff.w.r.t x
$\frac{dy}{dx}=e^x+e^{xlog(y)}(x \frac{dy}{dx}+log(y))$
$\frac{dy}{dx}=e^x+e^{xlog(y)}x \frac{dy}{dx}+e^{xlog(y)}log(y)$
$\frac{dy}{dx}= \frac{e^x+e^{xlog(y)}log(y)}{1-e^{xlog(y)}x}$