76.1.10 problem 10

Internal problem ID [17238]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 10
Date solved : Monday, March 31, 2025 at 03:45:36 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{1+y^{3}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=diff(y(x),x) = sec(x)^2/(1+y(x)^3); 
dsolve(ode,y(x), singsol=all);
 

\[ \tan \left (x \right )-\frac {y^{4}}{4}-y+c_1 = 0 \]

✓ Mathematica. Time used: 60.278 (sec). Leaf size: 1075

ode=D[y[x],x]==Sec[x]^2/(1+y[x]^3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/((y(x)**3 + 1)*cos(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out