88.9.7 problem 7

Internal problem ID [24027]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 48
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:54:35 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 20

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

\[ y = -\frac {\cos \left (x \right )}{2}+\frac {\sec \left (x \right )}{4}+\frac {\sqrt {2}\, \sec \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -\frac {1}{4} \left (\cos (2 x)-2 \sqrt {2}\right ) \sec (x) \end{align*}

✓ Sympy. Time used: 0.537 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*tan(x) - sin(x) + Derivative(y(x), x),0) 
ics = {y(pi/4): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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