Internal problem ID [2041]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-3 y-\left (3 y-x +2\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((x-3*y(x))=(3*y(x)-x+2)*diff(y(x),x),y(x), singsol=all)
\[ y = \frac {x}{3}+\frac {\operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {8 x}{3}} {\mathrm e}^{\frac {1}{3}} c_{1}}{3}\right )}{2}-\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 4.689 (sec). Leaf size: 43
DSolve[(x-3*y[x])==(3*y[x]-x+2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (3 W\left (-e^{-\frac {8 x}{3}-1+c_1}\right )+2 x-1\right ) y(x)\to \frac {1}{6} (2 x-1) \end{align*}