43.3.7 problem 3

Internal problem ID [8893]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:59:43 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=x^2*diff(y(x),x)+2*x*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x +c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \frac {x+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {C_{1} + x}{x^{2}} \]