y^{''}+14y^'+49y=e^{-7t}ln(t)

Lösung

y^{^{''}} + 14 y^{^{'}} + 49 y = e^{- 7 t} ln (t)

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} + \frac{2 e ^{- 7 t} t ^{2} ln ( t ) - 3 e ^{- 7 t} t ^{2}}{4}

Schritte zur Lösung

y^{''} (t) + 14 y^{'} (t) + 49 y = e^{- 7 t} ln (t)

Solve linear ODE:

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} + \frac{2 e ^{- 7 t} t ^{2} ln ( t ) - 3 e ^{- 7 t} t ^{2}}{4}

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} + \frac{2 e ^{- 7 t} t ^{2} ln ( t ) - 3 e ^{- 7 t} t ^{2}}{4}

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

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (t) - t e^{t}

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

y^{^{''}} + 4 y^{^{'}} + 8 y = x + e^{x}

y^{^{''}} + 4 y = 2 e^{2 t} + 4 cos (3 t)