Internal problem ID [15021]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 114.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (3 x -6 y+2\right ) y^{\prime }=1-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((x-2*y(x)-1)+(3*x-6*y(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {\operatorname {LambertW}\left (-3 \,{\mathrm e}^{\frac {5 x}{2}-\frac {5 c_{1}}{2}}\right )}{3}+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 4.144 (sec). Leaf size: 38
DSolve[(x-2*y[x]-1)+(3*x-6*y[x]+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (3 x-2 W\left (-e^{\frac {5 x}{2}-1+c_1}\right )\right ) \\ y(x)\to \frac {x}{2} \\ \end{align*}