Question

The general solution of the equation $\frac{dy}{dx}=1+xy$ is

• A. $y=c{e}^{-x^2/2}$
• B. $y=c{e}^{x^2/2}$
• C. $y(x+c)e^{-x^2/2}$
• D. None of these

Answer 1

Answer: (D)

$\frac{dy}{dx}=1+xy$
or $\frac{dy}{dx}-xy=1$
I.F. $=e^{\int -xdx}=e^{-x^2/2}$
Hence solution is $y\cdot e^{-x^2/2}$
$=\int e^{-x^2/2}dx+c$
$\int e^{-x^2/2}dx$ is not further integrable