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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\int \frac{x ^{2} + 3 x - 2}{x ^{2} - 1} d x

\frac{d}{d x} (\frac{1}{2 sin ( x )})

t an g e n t 2 sin (x)

\frac{\partial}{\partial m} (- m g (m) sin (a))

x \to 3 lim (\frac{27 - x}{x - 3})