26.3.7 problem 4(d)

Internal problem ID [4267]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(d)
Date solved : Monday, January 27, 2025 at 08:47:04 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 34

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

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