Question

The solution of $\frac{dy}{dx}=e^{2x-y}+x^3{e}^{-y}$ is:

• A. $e^y=e^{2x}+3x^2+c$
• B. $e^y=e^{2x}+\frac{x^4}{4}+c$
• C. $4e^y=2e^{2x}+x^4+c$
• D. $2e^y=e^{2x}+3x^4+c$

Answer 1

The correct option is C $4e^y=2e^{2x}+x^4+c$

$\frac{dy}{dx}=\frac{e^{2x}}{e^y}+\frac{x^3}{e^y}$

$\Rightarrow e^{y}dy=(e^{2x}+x^3)dx$

$\Rightarrow e^y=\frac{e^{2x}}{2}+\frac{x^4}{4}+\frac{c}{4}$

$\Rightarrow 4e^y=2e^{2x}+x^4+c$