67.1.41 problem 2.7 e

Internal problem ID [16306]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.7 e
Date solved : Thursday, October 02, 2025 at 10:45:34 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 8

ode:=x*diff(y(x),x) = sin(x); 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {Si}\left (x \right )+4 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 22

ode=x*D[y[x],x]==Sin[x]; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _0^x\frac {\sin (K[1])}{K[1]}dK[1]+4 \end{align*}

✓ Sympy. Time used: 0.234 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - sin(x),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {Si}{\left (x \right )} + 4 \]