y^{'''}+6y^{''}-16y^'=0

Lösung

y^{^{'''}} + 6 y^{^{''}} - 16 y^{^{'}} = 0

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

Schritte zur Lösung

y^{'''} (t) + 6 y^{''} (t) - 16 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

625 x^{^{''}} + 100 x^{^{'}} + 3 x = 0, x (0) = 25, x^{^{'}} (0) = - 2

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

16 y^{^{''}} - y = 0, y (- 4) = 1, y^{^{'}} (- 4) = - 1

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 6 - 6 e^{4}, y (1) = 0