Internal problem ID [15150]
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: 288.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (3 x +y+1\right ) y^{\prime }=-x -3} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 29
dsolve((x-y(x)+3)+(3*x+y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = 2-\frac {\left (x +1\right ) \left (\operatorname {LambertW}\left (-2 c_{1} \left (x +1\right )\right )-2\right )}{\operatorname {LambertW}\left (-2 c_{1} \left (x +1\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.771 (sec). Leaf size: 163
DSolve[(x-y[x]+3)+(3*x+y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2^{2/3} \left (x \left (-\log \left (\frac {3\ 2^{2/3} (y(x)+x-1)}{y(x)+3 x+1}\right )\right )+(x-1) \log \left (\frac {6\ 2^{2/3} (x+1)}{y(x)+3 x+1}\right )+\log \left (\frac {3\ 2^{2/3} (y(x)+x-1)}{y(x)+3 x+1}\right )+y(x) \left (\log \left (\frac {6\ 2^{2/3} (x+1)}{y(x)+3 x+1}\right )-\log \left (\frac {3\ 2^{2/3} (y(x)+x-1)}{y(x)+3 x+1}\right )+1\right )+3 x+1\right )}{9 (y(x)+x-1)}=\frac {1}{9} 2^{2/3} \log (9 (x+1))+c_1,y(x)\right ] \]