80.6.11 problem 9 (e)

Internal problem ID [18575]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 9 (e)
Date solved : Tuesday, January 28, 2025 at 12:00:46 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=1+\frac {2 y}{x -y} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 24

dsolve(diff(y(x),x)=1+2*y(x)/(x-y(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: 0.032 (sec). Leaf size: 36

DSolve[D[y[x],x]==1+2*y[x]/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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