35.2.1 problem 1

Internal problem ID [6093]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 1
Date solved : Sunday, March 30, 2025 at 10:38:21 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=3 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 7

ode:=x*diff(y(x),x) = y(x); 
ic:=y(2) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {3 x}{2} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 10

ode=x*D[y[x],x]==y[x]; 
ic={y[2]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 x}{2} \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - y(x),0) 
ics = {y(2): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 x}{2} \]