85.7.10 problem 1 (j)

Internal problem ID [22464]
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 : 1 (j)
Date solved : Thursday, October 02, 2025 at 08:40:20 PM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

\begin{align*} y \left (3\right )&=2 \\ \end{align*}

✗ Maple

ode:=diff(y(x),x) = 1/(x^2+4*y(x)^2-4)^(1/2); 
ic:=[y(3) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,1}]==1/Sqrt[x^2+4*y[x]^2-4]; 
ic={y[3]==2}; 
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/sqrt(x**2 + 4*y(x)**2 - 4),0) 
ics = {y(3): 2} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out