Internal problem ID [2054]
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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (2 x +3 y-1\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 53
dsolve((x+y(x))+(2*x+3*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {1}{2}+\frac {\sqrt {3}\, \left (x +1\right ) \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (\frac {\left (x +1\right )^{2}}{4}+\frac {\tan \left (\textit {\_Z} \right )^{2} \left (x +1\right )^{2}}{4}\right )+2 \sqrt {3}\, c_{1} +2 \textit {\_Z} \right )\right )}{6}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 73
DSolve[(x+y[x])+(2*x+3*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\arctan \left (\frac {\sqrt {3} (y(x)-1)}{3 y(x)+2 x-1}\right )}{\sqrt {3}}+\frac {1}{2} \log \left (\frac {3 \left (x^2+3 y(x)^2+3 (x-1) y(x)-x+1\right )}{(x+1)^2}\right )+\log (x+1)+c_1=0,y(x)\right ] \]