2.1.4 problem 4

Internal problem ID [654]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:05:01 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

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

\[ y = -\frac {1}{x}+6 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to 6-\frac {1}{x} \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = 6 - \frac {1}{x} \]