51.1.38 problem 38

Internal problem ID [10308]
Book : First order enumerated odes
Section : section 1
Problem number : 38
Date solved : Tuesday, September 30, 2025 at 07:19:16 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.231 (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)
 

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