36.2.14 problem 14

Internal problem ID [6307]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 14
Date solved : Monday, January 27, 2025 at 01:55:40 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(x*diff(y(x),x)+3*(y(x)+x^2)=sin(x)/x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sin \left (x \right )-x \cos \left (x \right )-\frac {3 x^{5}}{5}+c_{1}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 31

DSolve[x*D[y[x],x]+3*(y[x]+x^2)==Sin[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

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