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Beliebt Rechnen >

y^{''}-10y^'+25y=(4.5e^{5t})/(tt+1)

Lösung

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{4.5 e ^{5 t}}{tt + 1}

Lösung

y = c_{1} e^{5 t} + c_{2} t e^{5 t} - 2.25 e^{5 t} ln (t^{2} + 1) + 4.5 e^{5 t} t arctan (t)

Schritte zur Lösung

y^{''} (t) - 10 y^{'} (t) + 25 y = \frac{4.5 e ^{5 t}}{tt + 1}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} t e^{5 t} - 2.25 e^{5 t} ln (t^{2} + 1) + 4.5 e^{5 t} t arctan (t)

y = c_{1} e^{5 t} + c_{2} t e^{5 t} - 2.25 e^{5 t} ln (t^{2} + 1) + 4.5 e^{5 t} t arctan (t)

Graph

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