Internal problem ID [4442]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+\sin \relax (x )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x)+sin(x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\int -\frac {\sin \relax (x ) {\mathrm e}^{\frac {1}{x}}}{x^{2}}d x +c_{1}\right ) {\mathrm e}^{-\frac {1}{x}} \]
✓ Solution by Mathematica
Time used: 1.685 (sec). Leaf size: 38
DSolve[x^2*y'[x]+Sin[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}