83.46.3 problem Ex 3 page 69

Internal problem ID [19497]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 3 page 69
Date solved : Monday, March 31, 2025 at 07:26:06 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.249 (sec). Leaf size: 11

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

\[ y = -\sin \left (c_{1} \right ) x +c_{1} \]

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 20

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

\begin{align*} y(x)\to c_1 x-\arcsin (c_1) \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

NotImplementedError : multiple generators [_X0, tan(_X0*x/2)] 
No algorithms are implemented to solve equation -_X0 - 2*(1 - tan(_X0*x/2)**2)*tan(y(x)/2)/((tan(_X0*x/2)**2 + 1)*(tan(y(x)/2)**2 + 1)) + 2*(1 - tan(y(x)/2)**2)*tan(_X0*x/2)/((tan(_X0*x/2)**2 + 1)*(tan(y(x)/2)**2 + 1))