9y^{''}-y=xe^{x/3},y(0)=1,y^'(0)=0

Lösung

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y^{^{'}} (0) = 0

y = (- \frac{1}{8} + \frac{5}{8}) e^{\frac{x}{3}} + \frac{1}{8} 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 = (- \frac{1}{8} + \frac{5}{8}) e^{\frac{x}{3}} + \frac{1}{8} 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 = (- \frac{1}{8} + \frac{5}{8}) e^{\frac{x}{3}} + \frac{1}{8} 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}})

\frac{\partial}{\partial y} (\frac{y}{x} + 4 x)

\int (x^{2} + x^{5}) 3 x^{6} + 2 x^{3} d x

d er i v a t i v e - 3 x^{5}

\frac{d}{d x} (arcsec (3 x + 2))

x \to \frac{7 π}{2} - lim (sec (x))