y^{''}+2y^'+5y=0,y(0)=0,y^'(0)=-2

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = - 2

y = - e^{- t} sin (2 t)

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = - e^{- t} sin (2 t)

y = - e^{- t} sin (2 t)

16 \frac{d ^{4} y}{d x ^{4}} + 24 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

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

5 y^{^{''}} + y = 0

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

(D^{6} - 4 D^{4} + 4 D^{2}) y = 0