89.7.16 problem 16

Internal problem ID [24447]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:35:20 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.057 (sec). Leaf size: 42

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

\[ -\frac {\left (\sec \left (y\right )+\tan \left (y\right )\right ) \cos \left (2 x \right )}{2}+\frac {1}{\tan \left (\frac {y}{2}\right )-1}-\frac {2}{\tan \left (\frac {y}{2}\right )^{2}+1}+y+c_1 = 0 \]

✓ Mathematica. Time used: 0.48 (sec). Leaf size: 61

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

\[ \text {Solve}\left [2 \left (2 \sqrt {\cos ^2(y(x))} \sec (y(x)) \arcsin \left (\frac {\sqrt {1-\sin (y(x))}}{\sqrt {2}}\right )+\cos (y(x))\right )-\frac {2 \cos ^2(x) \cos (y(x))}{\sin (y(x))-1}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out