6.1.12 problem 5(a)

Internal problem ID [1530]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 5(a)
Date solved : Tuesday, September 30, 2025 at 04:35:23 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=\frac {\pi \sqrt {2}}{8} \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 8

ode:=diff(y(x),x) = cos(x)-y(x)*tan(x); 
ic:=[y(1/4*Pi) = 1/8*2^(1/2)*Pi]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \cos \left (x \right ) x \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 9

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

\begin{align*} y(x)&\to x \cos (x) \end{align*}

✓ Sympy. Time used: 0.267 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*tan(x) - cos(x) + Derivative(y(x), x),0) 
ics = {y(pi/4): sqrt(2)*pi/8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \cos {\left (x \right )} \]