32.2.30 problem 31

Internal problem ID [7747]
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 : Tuesday, September 30, 2025 at 05:04:24 PM
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*x*sin(x); 
ic:=[y(1/6*Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 34

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]
 

\begin{align*} y(x)&\to \sec (x) \int _{\frac {\pi }{6}}^x\cos (K[1]) (\cos (K[1])-2 K[1] \sin (K[1]))dK[1] \end{align*}

✓ Sympy. Time used: 0.759 (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)
 

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