y^{''}+6y^'+5y=12te^{5t}

Lösung

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 t e^{5 t}

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{e ^{5 t} t}{5} - \frac{4}{75} e^{5 t}

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 5 y = 12 t e^{5 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{e ^{5 t} t}{5} - \frac{4}{75} e^{5 t}

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + \frac{e ^{5 t} t}{5} - \frac{4}{75} e^{5 t}