y^'=2y^{''}

Lösung

y^{^{'}} = 2 y^{^{''}}

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

Schritte zur Lösung

y^{'} (t) = 2 y^{''} (t)

Solve linear ODE:

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

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

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

(D^{3} + 3 D^{2} + 3 D + 1) y = 0

y^{^{'''}} + 5 y^{^{''}} - 32 y^{^{'}} + 36 y = 0

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

6 y^{^{''}} - 8 y^{^{'}} + 6 y = 0