Internal problem ID [2485]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 7.
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 {x -2 y-3+\left (2 x +y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.64 (sec). Leaf size: 31
dsolve((x-2*y(x)-3)+(2*x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -1-\tan \left (\RootOf \left (-4 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -1\right )+2 c_{1}\right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 66
DSolve[(x-2*y[x]-3)+(2*x+y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [32 \text {ArcTan}\left (\frac {2 y(x)-x+3}{y(x)+2 x-1}\right )+8 \log \left (\frac {x^2+y(x)^2+2 y(x)-2 x+2}{5 (x-1)^2}\right )+16 \log (x-1)+5 c_1=0,y(x)\right ] \]