Internal problem ID [1925]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x +y\right ) y^{\prime }-y=-1-2 x} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 51
dsolve((2*x-y(x)+1)+(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{3}+\frac {\tan \left (\operatorname {RootOf}\left (\sqrt {2}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (3 x +1\right )^{2}\right )+\sqrt {2}\, \ln \left (2\right )+2 \sqrt {2}\, c_{1} -2 \textit {\_Z} \right )\right ) \sqrt {2}\, \left (-3 x -1\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 77
DSolve[(2*x-y[x]+1)+(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {-y(x)+2 x+1}{\sqrt {2} (y(x)+x)}\right )=2 \log \left (\frac {6 x^2+3 y(x)^2-2 y(x)+4 x+1}{(3 x+1)^2}\right )+4 \log (3 x+1)+3 c_1,y(x)\right ] \]