Internal problem ID [2009]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y+2 \left (x -2 y^{2}\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 41
dsolve([y(x)+2*(x-2*y(x)^2)*diff(y(x),x)=0,y(2) = -1],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 \sqrt {x^{2}-4}+2 x}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {2 \sqrt {x^{2}-4}+2 x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.237 (sec). Leaf size: 55
DSolve[{y[x]+2*(x-2*y[x]^2)*y'[x]==0,{y[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x-\sqrt {x^2-4}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {x^2-4}+x}}{\sqrt {2}} \\ \end{align*}