7.3.8 problem 8

Internal problem ID [48]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 8
Date solved : Friday, February 07, 2025 at 08:13:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(x),x)=2*x*sec(y(x)),y(x), singsol=all)
 

\[ y = \arcsin \left (x^{2}+2 c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.251 (sec). Leaf size: 12

DSolve[D[y[x],x]==2*x*Sec[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (x^2+c_1\right ) \]