Internal problem ID [7795]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 215.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (y+2 x -2\right ) y^{\prime }-y+x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 59
dsolve((y(x)+2*x-2)*diff(y(x),x)-y(x)+x+1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {3}{2}+\frac {\sqrt {3}\, \left (3 x -1\right ) \tan \left (\RootOf \left (\sqrt {3}\, \ln \left (\frac {3 \left (3 x -1\right )^{2}}{4}+\frac {3 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \left (3 x -1\right )^{2}}{4}\right )+2 \sqrt {3}\, c_{1}+6 \textit {\_Z} \right )\right )}{6}-\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 80
DSolve[(y[x]+2*x-2)*y'[x]-y[x]+x+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [6 \sqrt {3} \text {ArcTan}\left (\frac {4-3 y(x)}{\sqrt {3} (y(x)+2 x-2)}\right )=3 \log \left (\frac {3 x^2+3 y(x)^2+3 (x-3) y(x)-6 x+7}{(1-3 x)^2}\right )+6 \log (3 x-1)+2 c_1,y(x)\right ] \]