50.8.6 problem 1(f)

Internal problem ID [7922]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:32:29 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (-4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 36

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

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