85.15.14 problem 2 (d)

Internal problem ID [22539]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 2 (d)
Date solved : Thursday, October 02, 2025 at 08:48:42 PM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 2.173 (sec). Leaf size: 19

ode=D[y[x],x]==(2*Sin[2*x]-Tan[y[x]] )/( x*Sec[y[x]]^2 ); 
ic={y[Pi]==Pi/4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arctan \left (\frac {-\cos (2 x)+\pi +1}{x}\right ) \end{align*}

✗ Sympy

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

Timed Out