32.2.14 problem Differential equations with Linear Coefficients. Exercise 8.14, page 69

Internal problem ID [5798]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.14, page 69
Date solved : Monday, January 27, 2025 at 01:19:37 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 31

dsolve((x+y(x)+2)-(x-y(x)-4)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 58

DSolve[(x+y[x]+2)-(x-y[x]-4)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x+2}{y(x)-x+4}\right )+\log \left (\frac {x^2+y(x)^2+6 y(x)-2 x+10}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]