44.6.47 problem 47

Internal problem ID [7191]
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, February 04, 2025 at 12:46:13 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 17

DSolve[{x^3*D[y[x],x]+2*x^2*y[x]==10*Sin[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {10 (\text {Si}(1)-\text {Si}(x))}{x^2} \]