y^{''}-2y^'-3y=6xe^{2x}+4x-5

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x e^{2 x} + 4 x - 5

y = c_{1} e^{3 x} + c_{2} e^{- x} - 2 x e^{2 x} - \frac{4}{3} e^{2 x} - \frac{4 x}{3} + \frac{23}{9}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 3 y = 6 x e^{2 x} + 4 x - 5

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - 2 x e^{2 x} - \frac{4}{3} e^{2 x} - \frac{4 x}{3} + \frac{23}{9}

y = c_{1} e^{3 x} + c_{2} e^{- x} - 2 x e^{2 x} - \frac{4}{3} e^{2 x} - \frac{4 x}{3} + \frac{23}{9}

y^{^{''}} - y^{^{'}} - 2 y = sin (3 t)

y^{^{''}} + 6 y = 4 t^{2} - 3, y (0) = 0, y^{^{'}} (0) = - 7

y^{^{''}} + 10 y^{^{'}} + 16 y = 2581 cos (5 x)

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

y^{^{''}} + y^{^{'}} + \frac{1}{4} y = e^{x} (sin (3 x) - cos (3 x))