44.6.11 problem 11

Internal problem ID [7155]
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, February 04, 2025 at 12:40:43 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

DSolve[x*D[y[x],x]+4*y[x]==x^3-x,y[x],x,IncludeSingularSolutions -> True]
 

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