65.5.2 problem 2

Internal problem ID [15685]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:23:09 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x +\frac {1}{x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 14

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

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