y^{''}-8y^'+20y=100x^2+26xe^x

解答

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} + 2 x e^{x} + \frac{12}{13} e^{x}

求解步骤

y^{''} (x) - 8 y^{'} (x) + 20 y = 100 x^{2} + 26 x e^{x}

求解线性方程:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} + 2 x e^{x} + \frac{12}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} + 2 x e^{x} + \frac{12}{13} e^{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2}

y^{^{''}} - 2 y^{^{'}} = x^{2} - 1

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = sin (x)

y^{^{''}} + y = x + sin (x)

y^{^{''}} - 7 y^{^{'}} + 12 y = - 288 t^{3}