61. consider y =x^n sinx , where n is a positive integer.
a) Find dy/dx and d^2y / dx^2.
b) If x (d^2y / dx^2) -2(dy/dx) +xy =28 [x^ (n-1)] [sinx] + 2(n-1) x^n cos x, find the value of n.
更新1:
Ans for part a) dy/dx = x^n (cos x) + n [x^(n-1)] (sin x) d^2 y / dx^2 = [n (n-1) -x^2] x^ (n-2) sinx + 2n x^(n-1) cos x
