38.6.47 problem 47

Internal problem ID [8477]
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 : 47
Date solved : Tuesday, September 30, 2025 at 05:37:50 PM
CAS classification : [_linear]

\begin{align*} x^{3} y^{\prime }+2 x^{2} y&=10 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 17

ode:=x^3*diff(y(x),x)+2*x^2*y(x) = 10*sin(x); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {10 \,\operatorname {Si}\left (x \right )-10 \,\operatorname {Si}\left (1\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 25

ode=x^3*D[y[x],x]+2*x^2*y[x]==10*Sin[x]; 
ic={y[1]==0}; 
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]}{x^2} \end{align*}

✓ Sympy. Time used: 0.723 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x) + 2*x**2*y(x) - 10*sin(x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {10 \operatorname {Si}{\left (x \right )} - 10 \operatorname {Si}{\left (1 \right )}}{x^{2}} \]