73.5.6 problem 6.3 (b)

Internal problem ID [15117]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.3 (b)
Date solved : Tuesday, January 28, 2025 at 07:33:31 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 28

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

\begin{align*} y &= \sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ y &= -\sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 36

DSolve[D[y[x],x]==y[x]/x+x/y[x],y[x],x,IncludeSingularSolutions -> True]
 

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