Question

(e^2x+5)dy+ye^2xdx=0

Answer 1

$(e^{2x}+5)dy+ye^{2x}dx=0 \ frac{dy}{y}=-frac{e^{2x}dx}{e^{2x}+5}\ intfrac{dy}{y}=-intfrac{e^{2x}dx}{e^{2x}+5}\ ln | y|=-frac{1}{2}intfrac{d(e^{2x}+5)}{e^{2x}+5}$

 

$ln |y| =ln frac{1}{sqrt{e^{2x}+5}} + ln|C| \ y=frac{C}{sqrt{e^{2x}+5}}$