解微分方程y“+9y=sin3x 謝謝大家,速回,詳細過程答案y=c1sin3x+c2sin3x-1/6xsin3x

解微分方程y“+9y=sin3x 謝謝大家,速回,詳細過程答案y=c1sin3x+c2sin3x-1/6xsin3x

常數變易法先解y''+ 9y = 0其特徵方程為t²;+ 9 = 0t =±3i則通解為y = C1cos3x + C2sin3x現在令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 +…