(1+x^2)y'-2xy=(1+x^2)^2
Поделим уравнение на (1+x^2), получим
y'-2xy=(1+x^2)
y=uv y'=u'v+uv'
u'v+uv'-2x(uv)=(1+x^2)
(u'-2xu)v+uv'=1+x^2
(u'-2xu)=0
du/dx=2xu
int du/dx=2 int dx/x
ln[u]=2ln[x]
u=2x
uv'=1+x^2
2x*dv/dx=1+x^2
int dv=1/2 int (1+x^2)*dx/x
v=1/2ln[x]+x^2/2+C
y=2x(1/2ln[x]+x^2/2+C).