38.2.42 problem 42

Internal problem ID [6471]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 42
Date solved : Wednesday, March 05, 2025 at 12:51:17 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 17

ode:=diff(y(x),x)+y(x)/x = sin(x); 
ic:=y(1/2*Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 18

ode=D[y[x],x]+y[x]/x==Sin[x]; 
ic={y[Pi/2]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sin (x)-x \cos (x)-1}{x} \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x) + Derivative(y(x), x) + y(x)/x,0) 
ics = {y(pi/2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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