Internal problem ID [8013]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 433.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {\left (x y^{\prime }+y+2 x \right )^{2}-4 y x -4 x^{2}-4 a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 32
dsolve((x*diff(y(x),x)+y(x)+2*x)^2-4*x*y(x)-4*x^2-4*a = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2}+a}{x} \\ y \relax (x ) = c_{1}+\frac {\frac {c_{1}^{2}}{4}-a}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.201 (sec). Leaf size: 44
DSolve[-4*a - 4*x^2 - 4*x*y[x] + (2*x + y[x] + x*y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x} \\ y(x)\to -2 \sqrt {a} \\ y(x)\to 2 \sqrt {a} \\ \end{align*}