xdy/dx=y^3+y
dy/y(y^2+1)=dx/x
dy(1/y-y/(y^2+1)=dx/x
dy/y-ydy/(y^2+1)=dx/x
ln|y|-1/2ln|y^2+1|=ln|x|
ln(y/sqrt(y^2+1))=lnx
y/sqrt(y^2+1)=x+C
б) y=ux y'=u+u'x
du/(ulnu)=dx/x
ln(lnu)=lnx
x=lnu u=e^x y/x=e^x
y=e^x*x+C
xdy/dx=y^3+y
dy/y(y^2+1)=dx/x
dy(1/y-y/(y^2+1)=dx/x
dy/y-ydy/(y^2+1)=dx/x
ln|y|-1/2ln|y^2+1|=ln|x|
ln(y/sqrt(y^2+1))=lnx
y/sqrt(y^2+1)=x+C
б) y=ux y'=u+u'x
du/(ulnu)=dx/x
ln(lnu)=lnx
x=lnu u=e^x y/x=e^x
y=e^x*x+C