y'+2xy=x e^(-x^2)
[y=uv=>y'=u'v+uv']
u'v+uv'+2xuv=x e^(-x^2)
u'v+u(v'+2xv)=x e^(-x^2)
(*) v'+2xv=0 => dv/v=-2xdx => v=e^(-x^2)
u' e^(-x^2)=x e^(-x^2)
u'=x
u=(x^2)/2+C
y=((x^2)/2+C) e^(-x^2)
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y'+2xy=x e^(-x^2)
[y=uv=>y'=u'v+uv']
u'v+uv'+2xuv=x e^(-x^2)
u'v+u(v'+2xv)=x e^(-x^2)
(*) v'+2xv=0 => dv/v=-2xdx => v=e^(-x^2)
u' e^(-x^2)=x e^(-x^2)
u'=x
u=(x^2)/2+C
y=((x^2)/2+C) e^(-x^2)