(D^2-1)y=xe^{3x}

Lösung

(D^{2} - 1) y = x e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{8} - \frac{3}{32} e^{3 x}

Schritte zur Lösung

(D^{2} - 1) y = x e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{8} - \frac{3}{32} e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{8} - \frac{3}{32} e^{3 x}

y^{^{''}} - 2 y^{^{'}} + y = 15 e^{x}

y^{^{''}} + y^{^{'}} = 1, y (0) = 1, y^{^{'}} (0) = 1

D (x) = 72 - 1.8 x

y^{^{''}} + y^{^{'}} + y = 2 x e

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 6 t