9y^{''}-12y^'+4y=e^{-3x}

Lösung

9 y^{^{''}} - 12 y^{^{'}} + 4 y = e^{- 3 x}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

Schritte zur Lösung

9 y^{''} (x) - 12 y^{'} (x) + 4 y = e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

y = c_{1} e^{\frac{2 x}{3}} + c_{2} e^{\frac{2 x}{3}} x + \frac{1}{121} e^{- 3 x}

\int \frac{e ^{x}}{e ^{x} + e ^{2 x} - 2} d x

\frac{d}{d x} (x^{2} + 8)

\frac{\partial}{\partial y} (x e^{x y})

x \to 7 lim (tan (\frac{π x}{6}))

t an g e n t f (x) = 3 + 4 x^{2} - 2 x^{3}, (1, 5)