36.2.1 problem 1

Internal problem ID [6294]
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 : 1
Date solved : Monday, January 27, 2025 at 01:55:11 PM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x)+sin(x)-y(x)=0,y(x), singsol=all)
 

\[ y = \left (-\int \frac {\sin \left (x \right ) {\mathrm e}^{\frac {1}{x}}}{x^{2}}d x +c_{1} \right ) {\mathrm e}^{-\frac {1}{x}} \]

✓ Solution by Mathematica

Time used: 1.589 (sec). Leaf size: 38

DSolve[x^2*D[y[x],x]+Sin[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-1/x} \left (\int _1^x-\frac {e^{\frac {1}{K[1]}} \sin (K[1])}{K[1]^2}dK[1]+c_1\right ) \]