Consider the differential equation

where $y(0)=1.$

$y+1y^2=(y^5+1x)y^{\text{'}}$

Solve this equation by the following method: First, find a suitable integrating factor to obtain an implicit solution $F(x,y)=C.$ This implicit solution cannot be solved explicitly for $y$ but it can solved explicitly for $x$ :

$x=\frac{2y}{1+y}-y^5$