y^{'''}+7y^{''}+15y^'+9y=0

Lösung

y^{^{'''}} + 7 y^{^{''}} + 15 y^{^{'}} + 9 y = 0

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} t e^{- 3 t}

Schritte zur Lösung

y^{'''} (t) + 7 y^{''} (t) + 15 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} t e^{- 3 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} t e^{- 3 t}

4 y^{^{''}} + 3 y^{^{'}} = 0

\frac{d ^{3} y}{d x ^{3}} - 3 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0, y (0) = - 2, y (2) = 10

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 2