y^{''}-4y^'-12y=(4x+7)e^{-2x}

Lösung

y^{^{''}} - 4 y^{^{'}} - 12 y = (4 x + 7) e^{- 2 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{4} - \frac{15 e ^{- 2 x} x}{16}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) - 12 y = (4 x + 7) e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{4} - \frac{15 e ^{- 2 x} x}{16}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{4} - \frac{15 e ^{- 2 x} x}{16}

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

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 6 e^{2 x} + 16 x^{2}

y^{^{''}} + 4 y = \frac{3}{sin ( 2 x )}

a y^{^{''}} + 2 y^{^{'}} = 4 e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

(D^{2} + 3 D) y = - 18 x