Internal problem ID [8015]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 435.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-2 x y^{\prime } y-x +y \left (1+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)*(y(x)+1)-x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x \\ y \relax (x ) = c_{1} \sqrt {x}-\frac {c_{1}^{2} x}{4}+x -1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 55
DSolve[-x + y[x]*(1 + y[x]) - 2*x*y[x]*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {c_1{}^2 x}{4}-i c_1 \sqrt {x}-1 \\ y(x)\to x+\frac {c_1{}^2 x}{4}+i c_1 \sqrt {x}-1 \\ \end{align*}