15.2.18 problem 18

Internal problem ID [2888]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 18
Date solved : Monday, January 27, 2025 at 06:25:00 AM
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 )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 23

dsolve([diff(y(x),x)=(x+y(x))/(x-y(x)),y(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 33

DSolve[{D[y[x],x]==(x+y[x])/(x-y[x]),y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

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