y^{''}-17y^'+72y=0

Lösung

y^{^{''}} - 17 y^{^{'}} + 72 y = 0

y = c_{1} e^{9 t} + c_{2} e^{8 t}

Schritte zur Lösung

y^{''} (t) - 17 y^{'} (t) + 72 y = 0

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{8 t}

y = c_{1} e^{9 t} + c_{2} e^{8 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} = y^{^{'}}

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{4}{3}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{1} (0) = e^{2 x}

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