Internal problem ID [1950]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\frac {2 y x -1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((2*x*y(x)-1)/y(x)+(x+3*y(x))/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {x}{3 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x^{2}}{3}} c_{1} x}{3}\right )} \]
✓ Solution by Mathematica
Time used: 3.032 (sec). Leaf size: 37
DSolve[(2*x*y[x]-1)/y[x]+(x+3*y[x])/y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{3 W\left (\frac {1}{3} x e^{\frac {1}{3} \left (x^2-c_1\right )}\right )} y(x)\to 0 \end{align*}