8.3.8 problem 8

Internal problem ID [684]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:57:56 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: 0.244 (sec). Leaf size: 12

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

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