y^{''}-10y^'+61=0

Lösung

y^{^{''}} - 10 y^{^{'}} + 61 = 0

y = c_{1} e^{10 t} + c_{2} + \frac{61 t}{10}

Schritte zur Lösung

y^{''} (t) - 10 y^{'} (t) + 61 = 0

Solve linear ODE:

y = c_{1} e^{10 t} + c_{2} + \frac{61 t}{10}

y = c_{1} e^{10 t} + c_{2} + \frac{61 t}{10}

\frac{d ^{2} x}{d t ^{2}} + 9 \frac{d x}{d t} + 8 x = 2 t

y^{^{''}} - 7 y^{^{'}} + 14 y = - 2 e^{3 t}, y (0) = - 6

y^{^{''}} - 5 y^{^{'}} + 6 y = x e^{3 x}

y^{^{''}} + 4 y = - cos (3 x) - 2 sin (3 x)

y^{^{''}} - 9 y^{^{'}} = 5 e^{- 2 t}, y (0) = 1, y^{^{'}} (0) = 2