y^{''}-4y^'+4y=5e^{2x}

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = 5 e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{5 e ^{2 x} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = 5 e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{5 e ^{2 x} x ^{2}}{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{5 e ^{2 x} x ^{2}}{2}

y^{^{''}} + 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{(- 3)} e^{3} x

x^{^{''}} + 2 x + 3 x^{^{'}} = 5 cos (t) + sin (2 t)

(D^{2} + 2 D + 1) y = e^{- x}