38.1.27 problem 29

Internal problem ID [8188]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 05:18:29 PM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+x y&=10 \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=x^2*diff(y(x),x)+x*y(x) = 10*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {10 \,\operatorname {Si}\left (x \right )+c_1}{x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 28

ode=x^2*D[y[x],x]+x*y[x]==10*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\int _1^x\frac {10 \sin (K[1])}{K[1]}dK[1]+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.555 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + x*y(x) - 10*sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 10 \operatorname {Si}{\left (x \right )}}{x} \]