36y^{''}-y=xe^{x/6},y(0)=1,y^'(0)=0

Lösung

36 y^{^{''}} - y = x e^{\frac{x}{6}}, y (0) = 1, y^{^{'}} (0) = 0

y = \frac{1}{2} e^{\frac{x}{6}} - \frac{1}{4} e^{- \frac{x}{6}} + \frac{e ^{\frac{x}{6}} x ^{2}}{24} - \frac{e ^{\frac{x}{6}} ( x - 3 )}{4}

Schritte zur Lösung

36 y^{''} (x) - y = x e^{\frac{x}{6}}

Solve linear ODE:

y = \frac{1}{2} e^{\frac{x}{6}} - \frac{1}{4} e^{- \frac{x}{6}} + \frac{e ^{\frac{x}{6}} x ^{2}}{24} - \frac{e ^{\frac{x}{6}} ( x - 3 )}{4}

y = \frac{1}{2} e^{\frac{x}{6}} - \frac{1}{4} e^{- \frac{x}{6}} + \frac{e ^{\frac{x}{6}} x ^{2}}{24} - \frac{e ^{\frac{x}{6}} ( x - 3 )}{4}

f^{^{'}} (x) = 1

\int 64 x d x

t an g e n t 2 x^{3} + 8 x^{2} - 5 x + 9

a re a 8 - 2 x, x^{3} - 7 x^{2} + 12 x, [1, 4]

h \to 0 lim (h)