Question

求2x^2*y*y'=y^2+1的通解

Answer 1

设u=y^2

2x^2yy'=x^2d(y^2)/dx=x^2du/dx

x^2du/dx=u+1

du/(u+1)=dx/x^2

ln(u+1)=C-1/x

u=-1+e^(C-1/x)=-1+C'e^(-x)

y=sqrt(-1+C'e^(-x))