Answer
$y=1-7e^{-x^2/2}$
Work Step by Step
The standard form of the given equation is:
$y'+xy=x$ ....(1)
The integrating factor is: $e^{\int xdx}=e^{x^2/2}$
In order to determine the general solution, multiply equation (1) with the integrating factor and integrate both sides.
$\int ye^{x^2/2}=\int e^{x^2/2} x$
or, $y=1+ce^{-x^2/2}$ ...(2)
Applying the initial conditions in the above equation, we get
$ c=-7$
Thus, equation (2) becomes: $y=1-7e^{-x^2/2}$
