(dy)/(dx)+(2xy)/(x^2+1)=x

Lösung

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

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

y = \frac{x ^{4}}{4 ( x ^{2} + 1 )} + \frac{x ^{2}}{2 ( x ^{2} + 1 )} + \frac{c _{1}}{x ^{2} + 1}

t an g e n t \frac{3}{x ^{2}}

\int \frac{1}{x ^{2} x ^{2} + 9} d x

x \to 3 lim (7 x + ∣ x - 3 ∣)

\frac{\partial}{\partial x} (e^{y} + x e^{x y})

d er i v a t i v e x^{3} f (x)