Internal problem ID [15156]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 294.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x -y+3\right ) y^{\prime }=-x -2} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve((x-y(x)+2)+(x-y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = x -\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{5+4 x}\right )}{2}+\frac {5}{2} \]
✓ Solution by Mathematica
Time used: 3.14 (sec). Leaf size: 35
DSolve[(x-y[x]+2)+(x-y[x]+3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{4 x-1+c_1}\right )+x+\frac {5}{2} \\ y(x)\to x+\frac {5}{2} \\ \end{align*}