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Q.
The general solution of the equation $\frac{dy}{dx}=1+xy$ is
Differential Equations
Solution:
$\frac{dy}{dx}=1+xy$
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