56.3.29 problem 29

Internal problem ID [8887]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 29
Date solved : Wednesday, March 05, 2025 at 07:07:28 AM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

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

\[ y = \left (\frac {\pi }{2}+\arctan \left (x^{2}+2 c_{1} \right )\right ) x \]

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 22

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

\begin{align*} y(x)\to -x \cot ^{-1}\left (x^2-2 c_1\right ) \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

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