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Beliebt Rechnen >

y^{''}-2y^'+y=(e^t)/((1+t^2))

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} )}

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + y = \frac{e ^{t}}{( 1 + t ^{2} )}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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\int \frac{1}{x} e^{- x} d x

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d/(dt)(1/2 e^{-4t}cos(8t))

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