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Beliebt Rechnen >

9y^{''}-y=xe^{x/3}

Lösung

9 y^{^{''}} - y = x e^{\frac{x}{3}}

Lösung

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{e ^{\frac{x}{3}} x ^{2}}{12} - \frac{1}{8} e^{- \frac{x}{3}} (2 e^{\frac{2 x}{3}} x - 3 e^{\frac{2 x}{3}})

Schritte zur Lösung

9 y^{''} (x) - y = x e^{\frac{x}{3}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{e ^{\frac{x}{3}} x ^{2}}{12} - \frac{1}{8} e^{- \frac{x}{3}} (2 e^{\frac{2 x}{3}} x - 3 e^{\frac{2 x}{3}})

y = c_{1} e^{\frac{x}{3}} + c_{2} e^{- \frac{x}{3}} + \frac{e ^{\frac{x}{3}} x ^{2}}{12} - \frac{1}{8} e^{- \frac{x}{3}} (2 e^{\frac{2 x}{3}} x - 3 e^{\frac{2 x}{3}})

Graph

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