71.7.3 problem 3

Internal problem ID [14353]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 3
Date solved : Monday, March 31, 2025 at 12:19:01 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=2 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 7

ode:=diff(y(x),x) = y(x)/x; 
ic:=y(-1) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -2 x \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 8

ode=D[y[x],x]==y[x]/x; 
ic={y[-1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 x \]

✓ Sympy. Time used: 0.102 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - y(x)/x,0) 
ics = {y(-1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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