x+1(dy)/(dx)+(x+2)y=2xe^{-x}

Lösung

x + 1 \frac{d y}{d x} + (x + 2) y = 2 x e^{- x}

y = \frac{\int 2 e ^{\frac{x ^{2}}{2} + x} x - e ^{\frac{x ^{2}}{2} + 2 x} x d x}{e ^{\frac{x ^{2} + 4 x}{2}}}

Schritte zur Lösung

x + 1 \frac{d y}{d x} + (x + 2) y = 2 x e^{- x}

Solve linear ODE:

y = \frac{\int 2 e ^{\frac{x ^{2}}{2} + x} x - e ^{\frac{x ^{2}}{2} + 2 x} x d x}{e ^{\frac{x ^{2} + 4 x}{2}}}

y = \frac{\int 2 e ^{\frac{x ^{2}}{2} + x} x - e ^{\frac{x ^{2}}{2} + 2 x} x d x}{e ^{\frac{x ^{2} + 4 x}{2}}}

\int_{0}^{x} 1 + t^{2} d t

\frac{d}{d x} (4 x^{\frac{1}{4}})

x \to 3 lim (x - 1)

x \to 4 + lim (\frac{3}{( 4 - x ) ^{3}})

d er i v a t i v e g (x) = 7 - 3 x