23.1.13 problem 2(c)

Internal problem ID [4103]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 08:08:52 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {x \left (\ln \left (x \right )+c_{1} -2\right )}{\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {x (\log (x)-2+2 c_1)}{\log (x)+2 c_1} \\ y(x)\to x \\ \end{align*}