30.4.9 problem 9

Internal problem ID [7492]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.5, Special Integrating Factors. Exercises. page 69
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 04:39:35 PM
CAS classification : [_linear]

\begin{align*} x^{4}-x +y-x y^{\prime }&=0 \end{align*}

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

ode:=x^4-x+y(x)-x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x^{3}-3 \ln \left (x \right )+3 c_1 \right ) x}{3} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 22

ode=( x^4-x+y[x] )-( x )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.119 (sec). Leaf size: 14

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

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