64.7.12 problem 12

Internal problem ID [13386]
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
Date solved : Tuesday, January 28, 2025 at 05:36:33 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 5.743 (sec). Leaf size: 51

dsolve([(3*x-y(x)-6)+(x+y(x)+2)*diff(y(x),x)=0,y(2) = -2],y(x), singsol=all)
 

\[ y = -3-\tan \left (\operatorname {RootOf}\left (6 \sqrt {3}\, \ln \left (2\right )-3 \sqrt {3}\, \ln \left (3\right )-3 \sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (x -1\right )^{2}\right )+\pi +6 \textit {\_Z} \right )\right ) \sqrt {3}\, \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 90

DSolve[{(3*x-y[x]-6)+(x+y[x]+2)*D[y[x],x]==0,{y[2]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {\arctan \left (\frac {-y(x)+3 x-6}{\sqrt {3} (y(x)+x+2)}\right )}{\sqrt {3}}+\log (2)=\frac {1}{2} \log \left (\frac {3 x^2+y(x)^2+6 y(x)-6 x+12}{(x-1)^2}\right )+\log (x-1)+\frac {1}{18} \left (\sqrt {3} \pi +18 \log (2)-9 \log (4)\right ),y(x)\right ] \]