(d^2y)/(dx^2)-y=19.2e^{4x}+60e^x

解答

\frac{d ^{2} y}{d x ^{2}} - y = 19.2 e^{4 x} + 60 e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

求解步骤

\frac{d ^{2} y}{d x ^{2}} - y = 19.2 e^{4 x} + 60 e^{x}

求解线性方程:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{32}{25} e^{4 x} + 30 x e^{x}

y^{^{''}} - 16 y = 7 t, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 2 x = e^{t}

y^{^{''}} - y = sin (3 x)

5 y^{^{''}} - 19 y^{^{'}} - 4 y = 1 + 4 x

(d^{3} - 7 d - 6) y = 2 e^{x} cos (\frac{x}{2})