Internal problem ID [15171]
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: 309.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (2 x +2 y-1\right ) y^{\prime }=-1-x} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 20
dsolve([(x+y(x)+1)+(2*x+2*y(x)-1)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
\[ y = -x +\frac {3 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {1}{3}+\frac {x}{3}}}{3}\right )}{2}+2 \]
✓ Solution by Mathematica
Time used: 3.539 (sec). Leaf size: 28
DSolve[{(x+y[x]+1)+(2*x+2*y[x]-1)*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3}{2} W\left (\frac {2}{3} e^{\frac {x+1}{3}}\right )-x+2 \]