43.3.2 problem 1(b)

Internal problem ID [8888]
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 : 1(b)
Date solved : Tuesday, September 30, 2025 at 05:59:34 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=3 x^{3}-1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=x*diff(y(x),x)+y(x) = 3*x^3-1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {3}{4} x^{4}-x +c_1}{x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=x*D[y[x],x]+y[x]==3*x^3-1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x^3}{4}+\frac {c_1}{x}-1 \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3 + x*Derivative(y(x), x) + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {3 x^{3}}{4} - 1 \]