38.6.11 problem 11

Internal problem ID [8441]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 05:36:51 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+4 y&=x^{3}-x \end{align*}

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

ode:=x*diff(y(x),x)+4*y(x) = x^3-x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{7}-\frac {x}{5}+\frac {c_1}{x^{4}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 30

ode=x*D[y[x],x]+4*y[x]==x^3-x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\int _1^x\left (K[1]^6-K[1]^4\right )dK[1]+c_1}{x^4} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x*Derivative(y(x), x) + x + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{4}} + \frac {x^{3}}{7} - \frac {x}{5} \]