14.3.23 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 : Tuesday, September 30, 2025 at 06:48:47 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x)+y(x)/x = cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\cos \left (x \right )+\sin \left (x \right ) x +c_1}{x} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 18

ode=D[y[x],x]+1/x*y[x]==Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x \sin (x)+\cos (x)+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-cos(x) + Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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