y^{''}-2y^'+8y=0,y^'(0)=-6

Lösung

y^{^{''}} - 2 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = - 6

y = e^{t} ((- 6 - 7 c_{2}) cos (7 t) + c_{2} sin (7 t))

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{t} ((- 6 - 7 c_{2}) cos (7 t) + c_{2} sin (7 t))

y = e^{t} ((- 6 - 7 c_{2}) cos (7 t) + c_{2} sin (7 t))

16 y^{^{''}} + 40 y^{^{'}} + 169 y = 0, y (0) = 8, y^{^{'}} (0) = 18

y^{^{'''}} + 5 y^{^{''}} + 25 y^{^{'}} + 125 y = 0

\frac{d ^{2} y}{d t ^{2}} + 14 \frac{d y}{d t} + 48 y = 0

y^{^{''}} + 2 y^{^{''}} + 10 y = 0, y (0) = - 2, y^{^{'}} (0) = 0

2 y^{^{''}} + 9 y = 0