y^{''}-y^'-2y=5e^{4x}+6x

Lösung

y^{^{''}} - y^{^{'}} - 2 y = 5 e^{4 x} + 6 x

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{2} e^{4 x} - 3 x + \frac{3}{2}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 2 y = 5 e^{4 x} + 6 x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{2} e^{4 x} - 3 x + \frac{3}{2}

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{2} e^{4 x} - 3 x + \frac{3}{2}

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

y^{^{''}} + 10 y^{^{'}} + 25 y = x, y (0) = 0, y^{^{'}} (0) = 0

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

3 y^{^{''}} + 27 y = 2 cos (3 x)

(3 D^{2} + 3) y = 3 x