y^{''}-y^'-12y=e^2x+e^x-2

Lösung

y^{^{''}} - y^{^{'}} - 12 y = e^{2} x + e^{x} - 2

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{2} x}{12} + \frac{e ^{2}}{144} - \frac{1}{12} e^{x} + \frac{1}{6}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 12 y = e^{2} x + e^{x} - 2

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{2} x}{12} + \frac{e ^{2}}{144} - \frac{1}{12} e^{x} + \frac{1}{6}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{e ^{2} x}{12} + \frac{e ^{2}}{144} - \frac{1}{12} e^{x} + \frac{1}{6}

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2, y^{^{'}} (0) = 4

y^{^{''}} + y^{^{'}} - 12 y = \frac{e ^{x}}{x}

(6 D^{2} + 4 D + 2) y = x e^{- 2 x}

- 21 y + 4 y^{^{'}} + y^{^{''}} = t + 1

so l v e f or y, d (y) = 7 (2)^{y}