71.1.12 problem 26

Internal problem ID [14250]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 26
Date solved : Monday, March 31, 2025 at 12:14:16 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

ode:=x*diff(y(x),x)-sin(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {Si}\left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=x*D[y[x],x]-Sin[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.394 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} + \operatorname {Si}{\left (x \right )} \]