The general solution of the differential equation \(\frac{dy}{dx}=e^{x-y}+x^2e^{-y}\) is
Answer & explanation
Correct answer: option 1
\(\frac{dy}{dx}=e^{-y}(e^x+x^2)\)
so $\int e^ydy=\int e^x+x^2dx$
$⇒e^y=e^x+\frac{x^3}{3}+C$
The general solution of the differential equation \(\frac{dy}{dx}=e^{x-y}+x^2e^{-y}\) is
Correct answer: option 1
\(\frac{dy}{dx}=e^{-y}(e^x+x^2)\)
so $\int e^ydy=\int e^x+x^2dx$
$⇒e^y=e^x+\frac{x^3}{3}+C$