令x=cost,变换方程d^2y/dx^2-x/(1-x^2)*dy/dx+y/(1-x^2)=0

d^2y/dx^2=d(dy/dx)/dx=d(-dy/(sintdt))/(-sintdt)=(-(d^2y/dt*sint-dy/dt*cost)/(sint)^2)dt/(-sintdt)=d^2y/dt^2/(sint)^2-dy/dt*cost/(sint)^3原方程可化为1/(sint)^2*d^2y/dt^2-cost/(sint^3)*dy/dt+cost/(sint)...