y^'+xe^{(-x^2)/2}=0

Lösung

y^{^{'}} + x e^{\frac{- x ^{2}}{2}} = 0

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

Schritte zur Lösung

y^{'} (x) + x e^{\frac{- x ^{2}}{2}} = 0

Isoliere

y^{'} (x) : y^{'} (x) = - e^{- \frac{x ^{2}}{2}} x

Wenn

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

dann

f (x) = \int g (x) d x

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

\int - e^{- \frac{x ^{2}}{2}} x d x = e^{- \frac{x ^{2}}{2}} + c_{1}

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

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

\int \frac{5 ^{3 x}}{5 ^{3 x} + 7} d x

s l o p e - 3 x^{2} + 4 p + 4

\frac{d ^{3}}{d x ^{3}} (sin (2 x))

a re a x^{2} - 4 x, 0