Internal problem ID [2996]
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`]]
\[ \boxed {-y+\left (x +y+2\right ) y^{\prime }=6-3 x} \] With initial conditions \begin {align*} [y \left (2\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.828 (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)
\[ y \left (x \right ) = -3-\tan \left (\operatorname {RootOf}\left (-3 \sqrt {3}\, \ln \left (\left (x -1\right )^{2} \sec \left (\textit {\_Z} \right )^{2}\right )+6 \sqrt {3}\, \ln \left (2\right )-3 \sqrt {3}\, \ln \left (3\right )+\pi +6 \textit {\_Z} \right )\right ) \sqrt {3}\, \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.158 (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]
\[ \text {Solve}\left [\frac {\arctan \left (\frac {-y(x)+3 x-6}{\sqrt {3} (y(x)+x+2)}\right )}{\sqrt {3}}+\log (2)=\frac {1}{2} \log \left (\frac {3 x^2+y(x)^2+6 y(x)-6 x+12}{(x-1)^2}\right )+\log (x-1)+\frac {1}{18} \left (\sqrt {3} \pi +18 \log (2)-9 \log (4)\right ),y(x)\right ] \]