23.1.18 problem 2(h)

Internal problem ID [4108]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(h)
Date solved : Tuesday, March 04, 2025 at 05:26:18 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-2\right )&=5 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 20

ode:=diff(y(x),x) = x+1/x; 
ic:=y(-2) = 5; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

ode=D[y[x],x]==x+1/x; 
ic=y[-2]==5; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^2}{2}+\log \left (\frac {x}{2}\right )-i \pi +3 \]

✓ Sympy. Time used: 0.237 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + Derivative(y(x), x) - 1/x,0) 
ics = {y(-2): 5} 
dsolve(ode,func=y(x),ics=ics)
 

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