62.2.4 problem Ex 4

Internal problem ID [12735]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
Problem number : Ex 4
Date solved : Monday, March 31, 2025 at 06:57:34 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: 0.004 (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: 1.565 (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