y^{''}+6y^'-7y=3e^{2x}-2e^{3x}

Lösung

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 6 y^{'} (x) - 7 y = 3 e^{2 x} - 2 e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 7 x} + \frac{1}{3} e^{2 x} - \frac{1}{10} e^{3 x}

y^{^{'''}} - 4 y^{^{''}} + 13 y^{^{'}} = 104 e^{4 x}

y^{^{''}} + y^{^{'}} = 30, y (0) = - 94 t + 60 t^{2}

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

y^{^{''}} - 12 y^{^{'}} + 37 y = e^{6 x} - x^{2}

(D^{2} + 4 D + 3) y = 2 x e^{3 x} + 3 e^{3 x} cos (2 x)