解微分方程y"+9y=sin3x
问题描述：
解微分方程y"+9y=sin3x
谢谢大家,速回,详细过程答案y=c1sin3x+c2sin3x-1/6xsin3x
答
常数变易法先解y''+ 9y = 0其特征方程为t² + 9 = 0t = ±3i则通解为y = C1cos3x + C2sin3x现在令y''+ 9y = sin3x有形如y = f(x)cos3x + g(x)sin3x的解,且令y' = f(x)[cos3x]' + g(x)[sin3x]',得到f'(x)cos3x + ...