题目

设x=e^(-t) 试变换方程x^2 d^2y/dx^2 +xdy/dx+y=0

提问时间：2021-03-17

答案

x=e^(-t),即dx/dt= -e^(-t)那么dy/dx=(dy/dt) / (dx/dt)= -e^t *dy/dt,而d^2y/dx^2= [d(dy/dx) /dt] * dt/dx= [-e^t *d^2y/dt^2 -e^t *dy/dt] * (-e^t)=e^(2t) *d^2y/dt^2 +e^(2t) *dy/dt所以x^2 d^2y/dx^2= d^2y/dt...