y^{''}-16y=xe^x

Lösung

y^{^{''}} - 16 y = x e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

Schritte zur Lösung

y^{''} (x) - 16 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} - \frac{e ^{x} x}{15} - \frac{2}{225} e^{x}

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

y^{^{''}} - 3 y^{^{'}} + 5 y = 4 x^{3} - 2 x

y^{^{''}} - 8 y^{^{'}} + 16 y = 24 x + 2, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + 3 y = e^{- t} + sin (t)

\frac{d ^{2} y}{d x ^{2}} + 100 y = 1000 sin (10 x)