67.3.17 problem 4.5 (a)

Internal problem ID [16338]
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 : 4.5 (a)
Date solved : Thursday, October 02, 2025 at 01:21:02 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 11

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

\[ y = \sqrt {x^{2}+8} \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to \sqrt {x^2+8} \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \sqrt {x^{2} + 8} \]