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^{^{''}} - 2 y^{^{'}} + y = 10 cos (x) + 8 sin (x)

y^{^{''}} + 10 y^{^{'}} + 16 y = 949 sin (3 x)

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{- t}

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 50, y (0) = 0, y^{^{'}} (0) = 0