y^'+2xy=xe^{-x^2}

Lösung

y^{^{'}} + 2 x y = x e^{- x^{2}}

y = \frac{x ^{2}}{2 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{x ^{2}}{2 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

y = \frac{x ^{2}}{2 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

d er i v a t i v e 3 2690 - 10 x^{2}

\int 2 π x (x^{2} - 1)^{2} d x

\int_{4}^{9} \frac{4}{2 x} d x

d er i v a t i v e f (x) = 7 arctan (7 x), x = 1

n = 0 \sum \infty n^{2} (\frac{1}{3})^{n}