44.3.14 problem 2(d)

Internal problem ID [9124]
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(d)
Date solved : Tuesday, September 30, 2025 at 06:04:44 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 12

ode:=diff(y(x),x)-y(x)/x = x^2; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}+5\right ) x}{2} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

ode=D[y[x],x]-y[x]/x==x^2; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} x \left (x^2+5\right ) \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + Derivative(y(x), x) - y(x)/x,0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (\frac {x^{2}}{2} + \frac {5}{2}\right ) \]