73.6.1 problem 7.2

Internal problem ID [15140]
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
Date solved : Tuesday, January 28, 2025 at 07:36:33 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(diff(y(x),x)=1/y(x)-y(x)/(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 42

DSolve[D[y[x],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*}