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Beliebt Rechnen >

y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7

Lösung

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 7

Lösung

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

y = (\frac{5}{2} + \frac{1}{2}) e^{t} - \frac{5}{2} e^{- 2 t} - t - \frac{1}{2}

Graph

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\int \frac{- x - 8}{x ^{2} + 9} d x