Internal problem ID [1955]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve((x*y(x)+1)/y(x)+(2*y(x)-x)/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x^{2}}{4}} c_{1} x}{2}\right )} \]
✓ Solution by Mathematica
Time used: 3.516 (sec). Leaf size: 37
DSolve[(x*y[x]+1)/y[x]+(2*y[x]-x)/y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} x e^{\frac {1}{4} \left (x^2-2 c_1\right )}\right )} y(x)\to 0 \end{align*}