73.5.12 problem 6.6

Internal problem ID [15123]
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 : 6.6
Date solved : Tuesday, January 28, 2025 at 07:34:00 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.217 (sec). Leaf size: 13

dsolve([diff(y(x),x)-1/x*y(x)=1/y(x),y(1) = 3],y(x), singsol=all)
 

\[ y = \sqrt {x \left (11 x -2\right )} \]

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 20

DSolve[{D[y[x],x]-1/x*y[x]==1/y[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \sqrt {11 x-2} \]