Internal problem ID [7795]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 216.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (y-2 x +1\right ) y^{\prime }+y+x=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 59
dsolve((y(x)-2*x+1)*diff(y(x),x)+y(x)+x=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2}-\frac {\sqrt {3}\, \left (3 x -1\right ) \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (\frac {3 \left (3 x -1\right )^{2}}{4}+\frac {3 \tan \left (\textit {\_Z} \right )^{2} \left (3 x -1\right )^{2}}{4}\right )+2 \sqrt {3}\, c_{1} +6 \textit {\_Z} \right )\right )}{6}+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 82
DSolve[(y[x]-2*x+1)*y'[x]+y[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [6 \sqrt {3} \arctan \left (\frac {3 y(x)+1}{\sqrt {3} (-y(x)+2 x-1)}\right )=3 \log \left (\frac {3 x^2+3 y(x)^2-3 (x-1) y(x)-3 x+1}{(1-3 x)^2}\right )+6 \log (3 x-1)+2 c_1,y(x)\right ] \]