y^{''}-4y^'-5y=4x^2e^{2x}

解答

y^{^{''}} - 4 y^{^{'}} - 5 y = 4 x^{2} e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{4 e ^{2 x} x ^{2}}{9} - \frac{8}{81} e^{2 x}

求解步骤

y^{''} (x) - 4 y^{'} (x) - 5 y = 4 x^{2} e^{2 x}

求解线性方程:

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{4 e ^{2 x} x ^{2}}{9} - \frac{8}{81} e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{4 e ^{2 x} x ^{2}}{9} - \frac{8}{81} e^{2 x}

(d^{2} - 6 d + 9) \cdot y = x^{2} \cdot e^{2 x}

0.2 y^{^{''}} + 1.2 y^{^{'}} + 2 y = 5 cos (x)

(d^{4} - 2 d^{3} + d^{2}) y = x^{3}

d^{2} (d^{2} + 4) y = 96 x^{2} + sin^{2} (x) - k

(d^{2} + 3 d + 2) y = (e^{e})^{x}