44.3.11 problem 2(a)

Internal problem ID [9121]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 2(a)
Date solved : Tuesday, September 30, 2025 at 06:04:43 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-x y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 15

ode:=diff(y(x),x)-x*y(x) = 0; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 18

ode=D[y[x],x]-x*y[x]==0; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 e^{\frac {1}{2} \left (x^2-1\right )} \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 15

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)
 

\[ y{\left (x \right )} = \frac {3 e^{\frac {x^{2}}{2}}}{e^{\frac {1}{2}}} \]