8.5.4 problem 4

Internal problem ID [732]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 4
Date solved : Wednesday, February 05, 2025 at 03:51:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_1 \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 36

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

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