Internal problem ID [11707]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (2 x +y-1\right ) y^{\prime }=-x +3} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve((x-2*y(x)-3)+(2*x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -1-\tan \left (\operatorname {RootOf}\left (-4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (-1+x \right )+2 c_{1} \right )\right ) \left (-1+x \right ) \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 66
DSolve[(x-2*y[x]-3)+(2*x+y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [32 \arctan \left (\frac {2 y(x)-x+3}{y(x)+2 x-1}\right )+8 \log \left (\frac {x^2+y(x)^2+2 y(x)-2 x+2}{5 (x-1)^2}\right )+16 \log (x-1)+5 c_1=0,y(x)\right ] \]