79.1.21 problem 4 (iii)

Internal problem ID [18429]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 4 (iii)
Date solved : Thursday, March 13, 2025 at 11:56:50 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(x(t),t)-x(t)*tan(t) = 4*sin(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -2 \cos \left (t \right )+\sec \left (t \right ) c_{1} +\sec \left (t \right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 17

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

\[ x(t)\to \sec (t) (-\cos (2 t)+c_1) \]

✓ Sympy. Time used: 0.842 (sec). Leaf size: 12

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

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