67.3.11 problem 4.4 (a)

Internal problem ID [16332]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (a)
Date solved : Thursday, October 02, 2025 at 01:20:44 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(y(x),x) = x/y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {x^{2}+c_1} \\ y &= -\sqrt {x^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to -\sqrt {x^2+2 c_1}\\ y(x)&\to \sqrt {x^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 22

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} + x^{2}}\right ] \]