(D^2-4D+4)y=0

Lösung

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

25 x^{^{''}} - 20 x^{^{'}} + 4 x = 0

\frac{d ^{2} y}{d x ^{2}} = - k y

2 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 3

(d^{5} + 8 d^{3} + 16 d) y = 0