(d^2y)/(dt^2)+2(dy)/(dt)+10y=0

Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 10 y = 0

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 10 y = 0

Solve linear ODE:

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t))

3 \frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 11 y = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 0, y^{^{'}} (1) = e^{3}

(2 D^{4} - 3 D^{3} - 2 D^{2}) y = 0

\frac{1}{2} y^{^{''}} + 3 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = - \frac{5}{3}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 4, y^{^{'}} (0) = 14