79.1.21 problem 4 (iii)

Internal problem ID [18508]
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 : Tuesday, January 28, 2025 at 11:51:26 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]-x[t]*Tan[t]==4*Sin[t],x[t],t,IncludeSingularSolutions -> True]
 

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