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Beliebt Rechnen >

y^{''}-y=e^{-t},y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - y = e^{- t}, y (0) = 1, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

y^{''} (t) - y = e^{- t}

Solve linear ODE:

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

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

Graph

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