79.1.12 problem 2 (vi)

Internal problem ID [18499]
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 : 2 (vi)
Date solved : Tuesday, January 28, 2025 at 11:51:05 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 10

dsolve([diff(x(t),t)=tan(x(t)),x(0) = 1],x(t), singsol=all)
 

\[ x = \arcsin \left (\sin \left (1\right ) {\mathrm e}^{t}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 12

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

\[ x(t)\to \arcsin \left (e^t \sin (1)\right ) \]