x^{'''}+x^{''}-6x^'=0

Lösung

x^{^{'''}} + x^{^{''}} - 6 x^{^{'}} = 0

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

4 y^{^{''}} - y^{^{'}} + 17 y = 0

y^{^{''}} + \frac{4}{3} y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{10}{3}

y^{^{''}} + 15 y^{^{'}} = 0, y (0) = - 27, y^{^{'}} (0) = 15

625 y^{^{''}} + 729 y = 0, y (0) = 7, y^{^{'}} (0) = 3

l in e a r x^{^{''}} + 2 x^{^{'}} + 10 x = 0