85.7.16 problem 4 (d)

Internal problem ID [22470]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 32
Problem number : 4 (d)
Date solved : Thursday, October 02, 2025 at 08:40:25 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 64

ode:=diff(y(x),x) = 1/(x^2+4*y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {2 \operatorname {BesselJ}\left (-\frac {3}{4}, y^{2}\right ) y c_1 +\operatorname {BesselJ}\left (\frac {1}{4}, y^{2}\right ) c_1 x +2 \operatorname {BesselY}\left (-\frac {3}{4}, y^{2}\right ) y+\operatorname {BesselY}\left (\frac {1}{4}, y^{2}\right ) x}{2 \operatorname {BesselJ}\left (-\frac {3}{4}, y^{2}\right ) y+\operatorname {BesselJ}\left (\frac {1}{4}, y^{2}\right ) x} = 0 \]

✗ Mathematica

ode=D[y[x],{x,1}]==1/(x^2+4*y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x**2 + 4*y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - 1/(x**2 + 4*y(x)**2) cannot be solved by the lie group method