Internal problem ID [7803]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 223.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (2 y-x \right ) y^{\prime }-y-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.066 (sec). Leaf size: 53
dsolve((2*y(x)-x)*diff(y(x),x)-y(x)-2*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\frac {c_{1} x}{2}-\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ y \relax (x ) = \frac {\frac {c_{1} x}{2}+\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.207 (sec). Leaf size: 102
DSolve[(2*y[x]-x)*y'[x]-y[x]-2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+x\right ) \\ \end{align*}