74.1.54 problem 75

Internal problem ID [15834]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 75
Date solved : Tuesday, January 28, 2025 at 08:08:36 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 22

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

\[ y(x)\to \frac {\int _1^x\cos (K[1])dK[1]+c_1}{x} \]