Internal problem ID [11710]
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: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x +y+2\right ) y^{\prime }=-3 x +6} \] With initial conditions \begin {align*} [y \left (2\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 9.453 (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)
\[ y \left (x \right ) = -3-\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-3 \sqrt {3}\, \ln \left (3\right )+6 \sqrt {3}\, \ln \left (2\right )-3 \sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (-1+x \right )^{2}\right )+\pi +6 \textit {\_Z} \right )\right ) \left (-1+x \right ) \]
✓ Solution by Mathematica
Time used: 0.141 (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]
\[ \text {Solve}\left [\frac {\arctan \left (\frac {-y(x)+3 x-6}{\sqrt {3} (y(x)+x+2)}\right )}{\sqrt {3}}+\log (2)=\frac {1}{2} \log \left (\frac {3 x^2+y(x)^2+6 y(x)-6 x+12}{(x-1)^2}\right )+\log (x-1)+\frac {1}{18} \left (\sqrt {3} \pi +18 \log (2)-9 \log (4)\right ),y(x)\right ] \]