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

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 设x=e^(-t) 试变换方程x^2 d^2y/dx^2 +xdy/dx+y=0 已知参数方程x=t+t^2,y=cost.求导数dy/dx和d^2y/dx^2 参数方程：x=5(t-sint) y=5(1-cost) 求d^2y/dx^2 dy/dx我会求 设x=e^(-t),变换方程x^2*d^2y/dx^2+x*dy/dx+y=0设x=e^(-t),变换方程(x^2)*d^2y/dx^2+x*dy/dx+y=0答案是d^x/dt^2+y=0 x=(e^t)sint y=(e^t)cost 求d^2y/dx^2 x=lnsint y=cost+tsint的二阶导数d^2y/dx^2 求x=e^t*cost,y=e^t*sint所确定的函数的二阶导数,求讲解x't=(e^t)(sint+cost)y't=(e^t)(cost-sint)x''t=(e^t)(sint+cost+cost-sint)=2(e^t)costy''t=(e^t)(cost-sint-sint+cost)=-(e^t)sintdy/dx=(cost-sint)/(sint+cost)d^2 y/d(x^2)=d(dy/dx)/dx=(y''x 着急!作变换t=tanx,将微分方程cos^4x(d^2y/dx^2)+2cos^2x(1-sinxcosx)dy/dx+y=tanx,变成y关于t的方程,并求原来方程的通解. 作变换u=tany,x=e的t次幂 试将方程 x^2d^2y/dx^2+2x^2(tany)(dy/dx)^2+xdy/dx-sinycosy=0 化为u关于t的方 高数中若dy/dt=(dy/dx)*cost 那么d^2 y/dx^2 怎么求今天做题碰到的 结果为什么是d^2 y/dx^2*（cost）的平方-sintdy/dx 忘了说 x=sint 此参数方程为什么这么解x=2(t-cost)y=2(1-sint)求dy/dx.答案是dy/dx = -cost/(1+sint)为什么dx= 2(1+sint)dt为什么dy= -2cost 设x=e^(-t) 试变换方程x^2 d^2y/dx^2 +xdy/dx+y=0网上有种解法如下（网友franciscococo提供）：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] * ( 一道关于一元函数导数的问题把y看作自变量 ,x 为因变量 ,变换方程求证{(dy/dx) * [(dy)^3/d(x^3)]} - 3 {[(dy)^2/d(x^2)] ^2} = x dy/dx = (dx/dy) ^-1再由 复合函数求导法和反函数求导法做：(dy)^2/d(x^2) = d/dx[(dx/ 我有个疑问啊,就是那道设x=e^(-t) 试变换方程x^2 d^2y/dx^2 +xdy/dx+y=0,把X 已知x=t(1-cost),y=tcost,确定了y=f(x),求dy/dx和d^2y/dx^2, 设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2答案是-1／a(1-cost)^2 求由参数方程x=cost,y=sint所确定的函数y=y(x)的二阶导数.与求(d^2y)/(dx^2)的意思一样吗?