38.2.31 problem 31

Internal problem ID [6460]
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 : 31
Date solved : Sunday, March 30, 2025 at 11:02:06 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{6}\right )&=0 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 14

ode:=diff(y(x),x)-y(x)*tan(x) = cos(x)-2*sin(x)*x; 
ic:=y(1/6*Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \cos \left (x \right ) x -\frac {\pi \sec \left (x \right )}{8} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 25

ode=D[y[x],x]-y[x]*Tan[x]==Cos[x]-2*x*Sin[x]; 
ic={y[Pi/6]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} (4 x+4 x \cos (2 x)-\pi ) \sec (x) \]

✓ Sympy. Time used: 1.200 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*sin(x) - y(x)*tan(x) - cos(x) + Derivative(y(x), x),0) 
ics = {y(pi/6): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \cos {\left (x \right )} - \frac {\pi }{8 \cos {\left (x \right )}} \]