21.1.9 problem 9

Internal problem ID [4085]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 9
Date solved : Monday, January 27, 2025 at 08:08:00 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: 2.393 (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)
 

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

✓ Solution by Mathematica

Time used: 0.138 (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]
 

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