20.3.23 problem Problem 30

Internal problem ID [3632]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 30
Date solved : Monday, January 27, 2025 at 07:47:58 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve(diff(y(x),x)+1/x*y(x)=cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 18

DSolve[D[y[x],x]+1/x*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x \sin (x)+\cos (x)+c_1}{x} \]