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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = x e^{x^{2}} + 1

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

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

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

e x p an d 49 (2 + \frac{π}{4})

e x p an d \frac{27 x ^{\frac{4}{3}} + 3 ( x ^{3} + 5 )}{x ^{\frac{2}{3}}}

e x p an d (a - 3 e)^{2}

e x p an d (- 9 sin (t) + 9 sin (9 t))^{2}

e x p an d e^{- t} + (- 1 - e^{- t}) U (t - 5)