Internal problem ID [2487]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 9.
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 {3 x -y-6+\left (x +y+2\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = -2] \end {align*}
✓ Solution by Maple
Time used: 1.391 (sec). Leaf size: 120
dsolve([(3*x-y(x)-6)+(x+y(x)+2)*diff(y(x),x)=0,y(2) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {-3 \cos \left (\RootOf \left (-3 \sqrt {3}\, \ln \left (\frac {\left (x -1\right )^{2}}{\cos \left (\textit {\_Z} \right )^{2}}\right )+6 \sqrt {3}\, \ln \relax (2)-3 \sqrt {3}\, \ln \relax (3)+\pi +6 \textit {\_Z} \right )\right )+\left (1-x \right ) \sqrt {3}\, \sin \left (\RootOf \left (-3 \sqrt {3}\, \ln \left (\frac {\left (x -1\right )^{2}}{\cos \left (\textit {\_Z} \right )^{2}}\right )+6 \sqrt {3}\, \ln \relax (2)-3 \sqrt {3}\, \ln \relax (3)+\pi +6 \textit {\_Z} \right )\right )}{\cos \left (\RootOf \left (-3 \sqrt {3}\, \ln \left (\frac {\left (x -1\right )^{2}}{\cos \left (\textit {\_Z} \right )^{2}}\right )+6 \sqrt {3}\, \ln \relax (2)-3 \sqrt {3}\, \ln \relax (3)+\pi +6 \textit {\_Z} \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 90
DSolve[{(3*x-y[x]-6)+(x+y[x]+2)*y'[x]==0,y[2]==-2},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {ArcTan}\left (\frac {-y(x)+3 x-6}{\sqrt {3} (y(x)+x+2)}\right )}{\sqrt {3}}+\log (2)=\frac {1}{2} \log \left (\frac {3 x^2+y(x)^2+6 y(x)-6 x+12}{(x-1)^2}\right )+\log (x-1)+\frac {1}{18} \left (\sqrt {3} \pi +18 \log (2)-9 \log (4)\right ),y(x)\right ] \]