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Beliebt Rechnen >

y^{''}+5y^'+4y=13te^{4t}

Lösung

y^{^{''}} + 5 y^{^{'}} + 4 y = 13 t e^{4 t}

Lösung

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{13 e ^{4 t} t}{40} - \frac{169}{1600} e^{4 t}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 4 y = 13 t e^{4 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{13 e ^{4 t} t}{40} - \frac{169}{1600} e^{4 t}

y = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{13 e ^{4 t} t}{40} - \frac{169}{1600} e^{4 t}

Graph

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