Question

求个函数的二阶导数d^2y/dx^2

Answer 1

y’=k(-5x*sin5x+cos5x);

y’’=k[(-5x*5cosx-5sin5x) – 5sin5x]= k(-10sin5x-25xcos5x);

代入微分方程得：

k(-10sin5x-25xcos5x) + 25k*xcos5x = 20sin5x;

整理：

k*10sin5x=-20sin5x

由于对于定义域内任意x,等式恒成立

所以 k=-2;