试用自变量变换x=sint变换方程:(1-x^2)y''-xy'+a^2y=0（a为实数）答案是(d^2y/dt^2)+a^2y,..

Question

试用自变量变换x=sint变换方程:(1-x^2)y''-xy'+a^2y=0（a为实数）
答案是(d^2y/dt^2)+a^2y,..

Answer 1

设x=sint,y't=y'x*cost
,y"t=y"x*(cost)^2-y'x*sint
代入得:
y"t+sint*y'x-xy't+a^2y=0,即
y"t+a^2y=0