29.16.16 problem 459

Internal problem ID [5057]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 459
Date solved : Tuesday, March 04, 2025 at 07:48:52 PM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 37

ode:=(y(x)-cot(x)*csc(x))*diff(y(x),x)+csc(x)*(1+y(x)*cos(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \csc \left (x \right ) \left (-\sqrt {c_{1} +\cot \left (x \right )^{2}}+\cot \left (x \right )\right ) \\ y \left (x \right ) &= \csc \left (x \right ) \left (\sqrt {c_{1} +\cot \left (x \right )^{2}}+\cot \left (x \right )\right ) \\ \end{align*}

✓ Mathematica. Time used: 1.484 (sec). Leaf size: 85

ode=(y[x]-Cot[x] Csc[x])D[y[x],x]+Csc[x](1+y[x] Cos[x])y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \cot (x) \csc (x)-\frac {i \csc ^2(x) \sqrt {(-1+c_1) \cos (2 x)-1-c_1}}{\sqrt {2}} \\ y(x)\to \cot (x) \csc (x)+\frac {i \csc ^2(x) \sqrt {(-1+c_1) \cos (2 x)-1-c_1}}{\sqrt {2}} \\ \end{align*}

✗ Sympy

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

Timed Out