y^{'''}+3y^{''}-4y=xe^x+14x

Lösung

y^{^{'''}} + 3 y^{^{''}} - 4 y = x e^{x} + 14 x

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} + \frac{e ^{x} x ^{2}}{18} - \frac{2 e ^{x} x}{27} - \frac{7 x}{2}

Schritte zur Lösung

y^{'''} (x) + 3 y^{''} (x) - 4 y = x e^{x} + 14 x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} + \frac{e ^{x} x ^{2}}{18} - \frac{2 e ^{x} x}{27} - \frac{7 x}{2}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} + \frac{e ^{x} x ^{2}}{18} - \frac{2 e ^{x} x}{27} - \frac{7 x}{2}

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

y^{^{''}} + y^{^{'}} + 0.25 y = e^{x} (sin (3 x) - cos (3 x))

y^{^{''}} + 4 y^{^{'}} = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 9

y^{^{''}} + 4 y^{^{'}} = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} + y = t^{2} sin (t)