dy/dx=y/y²+1

dy/dx = y/(y² + 1) /*dx dy = y/(y² + 1)dx /* (y² + 1) (y² + 1)dy = ydx /:y (y² + 1)/ydy = dx (y + 1/y)dy = dx ∫(y + 1/y)dy = ∫dx 0,5y² + ln|y| = x /*2 y² + 2ln|y| = 2x y² + ln|y²| = 2x + C

dy/dx = y/(y² +1) /*dx dy = y/(y² +1)dx /* (y² +1) (y² +1)dy = ydx /:y (y² +1)/ydy = dx (y +1/y)dy = dx ∫(y +1/y)dy = ∫dx 0,5y² + ln|y| = x /*2 y² +2ln|y| = 2x y² +ln|y²| = 2x + C