10y^{''}+30y^'+20y=0

Lösung

10 y^{^{''}} + 30 y^{^{'}} + 20 y = 0

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

Schritte zur Lösung

10 y^{''} (t) + 30 y^{'} (t) + 20 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 0

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 5

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 5