2.3.8 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 : Tuesday, September 30, 2025 at 04:05:57 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 12

ode=D[y[x],x]==2*x*Sec[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin \left (x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x/cos(y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (C_{1} + x^{2} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (C_{1} + x^{2} \right )}\right ] \]