Answer
$y=-\dfrac{e^{x^2}}{(x+1)}+6e^{x^2}$
Work Step by Step
The standard form of the given equation is:
$y'-2xy=\dfrac{e^{x^2}}{(x+1)^2}$ ....(1)
The integrating factor is: $e^{\int -(-2x)dx}=e^{-x^2}$
In order to determine the general solution, multiply equation (1) with the integrating factor and integrate both sides.
$y=-\dfrac{e^{x^2}}{(x+1)}+ce^{x^2}$ ...(2)
Applying the initial conditions in the above equation, we get
$ c=6$
Thus, equation (2) becomes: $y=-\dfrac{e^{x^2}}{(x+1)}+6e^{x^2}$
