50.8.13 problem 2(e)

Internal problem ID [7929]
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 : 2(e)
Date solved : Monday, January 27, 2025 at 03:32:50 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.171 (sec). Leaf size: 30

dsolve([diff(y(x),x)=(x+y(x))/(x-y(x)),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 46

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

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