如何求微分方程(√1-x^2)y`=√1-y^2和x*dy/dx-yIny=0的通解?

Question

如何求微分方程(√1-x^2)y`=√1-y^2和x*dy/dx-yIny=0的通解?

Answer 1

(√1-x^2)y'=√1-y^2
dy/√1-y^2=dx/√1-x^2
积分得通
arcsiny=arcsinx+C或 y=sin(arcsinx+C)
x*dy/dx-yIny=0
dy/[yIny]=dx/x
积分得通
lnlny=lnx+lnC
lny=Cx
y=e^(Cx)