79.1.6 problem 1 (vi)

Internal problem ID [18493]
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 : 1 (vi)
Date solved : Tuesday, January 28, 2025 at 11:50:52 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 13

dsolve([diff(x(t),t)=cos(t)/sin(t),x(1) = 0],x(t), singsol=all)
 

\[ x = \ln \left (\sin \left (t \right )\right )-\ln \left (\sin \left (1\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 11

DSolve[{D[x[t],t]==Cos[t]/Sin[t],{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \log (\csc (1) \sin (t)) \]