$dy/dx = e^{-x^2} - 2xy $
$y(0) = 1$
expressing in the form $y = f(x)$
I was thinking of seperation of variable and the integrating factor method but I don't think it will work.
What should I do this?
$dy/dx = e^{-x^2} - 2xy $
$y(0) = 1$
expressing in the form $y = f(x)$
I was thinking of seperation of variable and the integrating factor method but I don't think it will work.
What should I do this?
WolframAlpha solves your problem quite perfectly:
$\frac{dy}{dx}+2xy=e^{-x^2}$
Multiplying by $e^{x^2}$:
$\frac{dy}{dx}e^{x^2}+(2e^{x^2}x)y=1$
The left side is $(e^{x^2}y)'$:
$(e^{x^2}y)'=1$
Integrate both sides with respect to $x$ and you have:
$e^{x^2}y(x)=x+C$
The only thing you need to do is using $y(0)=1$ to get rid of the constant. Put $x=0$ and $y=1$ to get $C$.