y^{''}+7y^'+12y=t^2e^{-3t}

Lösung

y^{^{''}} + 7 y^{^{'}} + 12 y = t^{2} e^{- 3 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{e ^{- 3 t} t ^{3}}{3} - e^{- 3 t} t^{2} + 2 t e^{- 3 t}

Schritte zur Lösung

y^{''} (t) + 7 y^{'} (t) + 12 y = t^{2} e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{e ^{- 3 t} t ^{3}}{3} - e^{- 3 t} t^{2} + 2 t e^{- 3 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 4 t} + \frac{e ^{- 3 t} t ^{3}}{3} - e^{- 3 t} t^{2} + 2 t e^{- 3 t}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x} tan (x)

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

(d^{4} + d^{2}) y = 18 x - 4 sin (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{2} + e^{x}