32.2.36 problem 37

Internal problem ID [7753]
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 : 37
Date solved : Tuesday, September 30, 2025 at 05:04:41 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 25

ode:=diff(y(x),x)+y(x)/x = sin(2*x); 
ic:=[y(1/4*Pi) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {-2 \cos \left (2 x \right ) x +\sin \left (2 x \right )+2 \pi -1}{4 x} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 35

ode=D[y[x],x]+1/x*y[x]==Sin[2*x]; 
ic={y[Pi/4]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \int _{\frac {\pi }{4}}^xK[1] \sin (2 K[1])dK[1]+\pi }{2 x} \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(2*x) + Derivative(y(x), x) + y(x)/x,0) 
ics = {y(pi/4): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\cos {\left (2 x \right )}}{2} + \frac {\sin {\left (2 x \right )}}{4 x} + \frac {- \frac {1}{4} + \frac {\pi }{2}}{x} \]