y^{'''}-4y^'=xe^{2x}+x^2+sin(x)

解答

y^{^{'''}} - 4 y^{^{'}} = x e^{2 x} + x^{2} + sin (x)

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}

求解步骤

y^{'''} (x) - 4 y^{'} (x) = x e^{2 x} + x^{2} + sin (x)

求解线性方程:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}