29.7.24 problem 199

Internal problem ID [4799]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 199
Date solved : Sunday, March 30, 2025 at 03:58:22 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 16

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

\[ y = \arctan \left (\frac {x^{3}+2 c_1}{x}\right ) \]

✓ Mathematica. Time used: 1.923 (sec). Leaf size: 53

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

\begin{align*} y(x)\to \arctan \left (x^2+\frac {c_1}{2 x}\right ) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ y(x)\to \frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (3*x**2*cos(2*y(x)) + 3*x**2 - sin(2*y(x)))/(2*x) cannot be solved by the factorable group method