2y^{''}-y^'-y=5xe^{2x}

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

4 y^{^{''}} - 40 y^{^{'}} + 100 y = 2 sin (2 x) + 5 cos (2 x)

y^{^{''}} - 4 y + 5 = 0

4 y^{^{''}} - y = 1, y^{^{'}} (0) = \frac{1}{2}, y (0) = 0

y^{^{''}} - y^{^{'}} - 20 = 0

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{3 x} cos (2 x) + e^{2 x}