9.1.14 problem 14

Internal problem ID [2854]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 05:54:58 AM
CAS classification : [_separable]

\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 11

ode:=sin(x)*cos(y(x))^2+cos(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\arctan \left (\sec \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 1.024 (sec). Leaf size: 31

ode=Sin[x]*Cos[y[x]]^2+Cos[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arctan (-\sec (x)+c_1)\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2} \end{align*}

✗ Sympy

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

Timed Out