72.1.21 problem 24

Internal problem ID [14621]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 06:44:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sec \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 8

dsolve(diff(y(x),x)=sec(y(x)),y(x), singsol=all)
 

\[ y = \arcsin \left (x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 22

DSolve[D[y[x],x]==Sec[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ][x+c_1] \]