(1+x^2)d(dy/dx)/dx=1+(dy/dx)^2求通解

Question

(1+x^2)d(dy/dx)/dx=1+(dy/dx)^2求通解

Answer 1

令u=dy/dx
du/(1+u^2)=dx/(1+x^2)
arctanu=arctanx+arctanC1
u=(x+C1)/(1-C1·x)
y=∫(x+C1)/(1-C1·x)dx+C2
……