验证参数方程{x=e^t*sint y=e^t*cost 所确定的函数满足关系式(d^2y/dx^2)*(x+y)^2=2(x*dy/dx-y)

题目

验证参数方程{x=e^t*sint y=e^t*cost 所确定的函数满足关系式(d^2y/dx^2)*(x+y)^2=2(x*dy/dx-y)
这两个式子我怎么算都不相等

答案

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