y^{''}-4y^'-12y=3x^2-5x+4-3e^{-3x}

Lösung

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 x^{2} - 5 x + 4 - 3 e^{- 3 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} + \frac{7 x}{12} - \frac{41}{72} - \frac{1}{3} e^{- 3 x}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) - 12 y = 3 x^{2} - 5 x + 4 - 3 e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} + \frac{7 x}{12} - \frac{41}{72} - \frac{1}{3} e^{- 3 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} + \frac{7 x}{12} - \frac{41}{72} - \frac{1}{3} e^{- 3 x}

y^{^{''}} + y = 2 e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 15 e^{3 t}, y (0) = 2, y^{^{'}} (0) = - 6

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

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

y^{^{''}} + 2 y^{^{'}} + y = \frac{1}{6} e^{- x}