67.5.12 problem 6.6

Internal problem ID [16410]
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 : Thursday, October 02, 2025 at 01:29:03 PM
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*}

✓ Maple. Time used: 0.122 (sec). Leaf size: 13

ode:=diff(y(x),x)-y(x)/x = 1/y(x); 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \sqrt {x} \sqrt {11 x-2} \end{align*}

✓ Sympy. Time used: 0.220 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/y(x) - y(x)/x,0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

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