y^{''}-5y^'+6y=xe^x

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = x e^{x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 6 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{e ^{x} x}{2} + \frac{3}{4} e^{x}

\int \frac{e ^{6 x}}{e ^{6 x} - 3 e ^{- 6 x}} d x

\int \frac{8 y}{x} d x

x \to \infty lim (\frac{3.4}{0.1 + 33.9 e ^{- 0.5678 x}})

l a pl a ce t r an s f or m t^{3} 1 (t)

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})