Internal problem ID [13381]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{x}-\frac {x}{y}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve(diff(y(x),x)=y(x)/x+x/y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ y \left (x \right ) &= -\sqrt {2 \ln \left (x \right )+c_{1}}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 36
DSolve[y'[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*}