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

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令x=cost,变换方程d^2y/dx^2-x/(1-x^2)*dy/dx+y/(1-x^2)=0
答案是d^2y/dt^2+y=0,想看看解法

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)^2*dy/(sintdt)+y/(sint)^2=0
z/(sint)^2*d^y/dt^2+y/(sint)^2=0,即d^2y/dt^2+y=0

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