y^{''}-8y^'-20y=5e^{-2x}

Lösung

y^{^{''}} - 8 y^{^{'}} - 20 y = 5 e^{- 2 x}

y = c_{1} e^{10 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{12}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) - 20 y = 5 e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{10 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{12}

y = c_{1} e^{10 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{12}

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

y^{^{''}} + 9 y^{^{'}} = sin (t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 9 y = 5 sin (3 x), y (0) = 6, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 3 e^{x}

y^{^{''}} - 6 y^{^{'}} + 13 y = 4.29 e^{3 t} \cdot cos (4.29 t)