Internal problem ID [13404]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {1}{y}+\frac {y}{2 x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)=1/y(x)-y(x)/(2*x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {x \left (x^{2}+c_{1} \right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (x^{2}+c_{1} \right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 42
DSolve[y'[x]==1/y[x]-y[x]/(2*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ \end{align*}