2t^{(4)}-y^{'''}-9y^{''}+4y^'+4y=0

Lösung

2 t^{(4)} - y^{^{'''}} - 9 y^{^{''}} + 4 y^{^{'}} + 4 y = 0

y = c_{1} e^{- 0.48973 \dots t} + c_{2} e^{0.87067 \dots t} + c_{3} e^{- 9.38094 \dots t} - \frac{t ^{4}}{2} + 2 t^{3} - \frac{39 t ^{2}}{2} + 63 t - \frac{591}{4}

Schritte zur Lösung

2 t^{(4)} - y^{'''} (t) - 9 y^{''} (t) + 4 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = c_{1} e^{- 0.48973 \dots t} + c_{2} e^{0.87067 \dots t} + c_{3} e^{- 9.38094 \dots t} - \frac{t ^{4}}{2} + 2 t^{3} - \frac{39 t ^{2}}{2} + 63 t - \frac{591}{4}

y = c_{1} e^{- 0.48973 \dots t} + c_{2} e^{0.87067 \dots t} + c_{3} e^{- 9.38094 \dots t} - \frac{t ^{4}}{2} + 2 t^{3} - \frac{39 t ^{2}}{2} + 63 t - \frac{591}{4}

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 e^{x} + 10 e^{5 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

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

y^{^{''}} - 3 y^{^{'}} = 1

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