29.17.17 problem 476

Internal problem ID [5074]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 476
Date solved : Sunday, March 30, 2025 at 06:35:23 AM
CAS classification : [_separable]

\begin{align*} 3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 22

ode:=3*y(x)*diff(y(x),x)+5*cot(x)*cot(y(x))*cos(y(x))^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (\sin \left (x \right )\right )+c_1 -\frac {3 \tan \left (y\right )}{10}+\frac {3 y \sec \left (y\right )^{2}}{10} = 0 \]

✓ Mathematica. Time used: 0.486 (sec). Leaf size: 30

ode=3 y[x] D[y[x],x]+5 Cot[x] Cot[y[x]] Cos[y[x]]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [40 \sin (x) e^{\frac {3}{10} \left (y(x) \sec ^2(y(x))-\tan (y(x))\right )}=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.728 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), x) + 5*cos(y(x))**2/(tan(x)*tan(y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {y \tan {\left (y \right )}}{\cos ^{2}{\left (y \right )}}\, dy = C_{1} - \frac {5 \log {\left (\sin {\left (x \right )} \right )}}{3} \]