81.4.7 problem 5-8

Internal problem ID [21521]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-8
Date solved : Thursday, October 02, 2025 at 07:46:43 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(x(t),t)-tan(t)*x(t) = sin(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {\cos \left (t \right )}{2}+c_1 \sec \left (t \right )+\frac {\sec \left (t \right )}{4} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 17

ode=D[x[t],t]-Tan[t]*x[t]==Sin[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\frac {\cos (t)}{2}+c_1 \sec (t) \end{align*}

✓ Sympy. Time used: 0.549 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-x(t)*tan(t) - sin(t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {C_{1}}{\cos {\left (t \right )}} - \frac {\cos {\left (t \right )}}{2} \]