85.1.20 problem 12 (a)

Internal problem ID [22425]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 12 (a)
Date solved : Thursday, October 02, 2025 at 08:39:12 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-\frac {4}{x^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 13

ode:=diff(y(x),x) = -4/x^2; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4-2 x}{x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=D[y[x],{x,1}]==-4/x^2; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4}{x}-2 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 4/x**2,0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = -2 + \frac {4}{x} \]