y^{''}+2y^'+y=e^{-x}ln(x)

Lösung

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} ln (x)

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

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + y = e^{- x} ln (x)

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{x ^{6}}{6} - \frac{x ^{5}}{5} + 20)

a re a f (x) = x, g (x) = x, x = 0, x = 2

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

n = 1 \sum \infty \frac{1}{n ^{3}}

\int 10 cos (100 x) d x