y^{''}-324y=0

Lösung

y^{^{''}} - 324 y = 0

y = c_{1} e^{18 t} + c_{2} e^{- 18 t}

Schritte zur Lösung

y^{''} (t) - 324 y = 0

Solve linear ODE:

y = c_{1} e^{18 t} + c_{2} e^{- 18 t}

y = c_{1} e^{18 t} + c_{2} e^{- 18 t}

49 y^{^{''}} + 56 y^{^{'}} + 16 y = 0

y^{^{''}} + y^{^{'}} - 15 y = 0

y^{^{''''}} - 4 y^{^{'''}} + 5 y^{^{''}} - 4 y^{^{'}} + 4 y = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 0

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 2