Internal problem ID [1943]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (x -2 y\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve((x+y(x))+(x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \frac {\frac {c_{1} x}{2}-\frac {\sqrt {3 c_{1}^{2} x^{2}+2}}{2}}{c_{1}} y = \frac {\frac {c_{1} x}{2}+\frac {\sqrt {3 c_{1}^{2} x^{2}+2}}{2}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.535 (sec). Leaf size: 106
DSolve[(x+y[x])+(x-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {3 x^2-2 e^{2 c_1}}\right ) y(x)\to \frac {1}{2} \left (x+\sqrt {3 x^2-2 e^{2 c_1}}\right ) y(x)\to \frac {1}{2} \left (x-\sqrt {3} \sqrt {x^2}\right ) y(x)\to \frac {1}{2} \left (\sqrt {3} \sqrt {x^2}+x\right ) \end{align*}