85.7.6 problem 1 (f)

Internal problem ID [22460]
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 (f)
Date solved : Thursday, October 02, 2025 at 08:39:57 PM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.150 (sec). Leaf size: 107

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

\[ y = \operatorname {RootOf}\left (\operatorname {BesselI}\left (-\frac {3}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \textit {\_Z} \operatorname {BesselK}\left (\frac {1}{4}, 2\right )-2 \operatorname {BesselI}\left (-\frac {3}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \textit {\_Z} \operatorname {BesselK}\left (\frac {3}{4}, 2\right )+\operatorname {BesselI}\left (\frac {1}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselK}\left (\frac {1}{4}, 2\right ) x -2 \operatorname {BesselI}\left (\frac {1}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselK}\left (\frac {3}{4}, 2\right ) x -\operatorname {BesselK}\left (\frac {1}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselI}\left (\frac {1}{4}, 2\right ) x -2 \operatorname {BesselK}\left (\frac {1}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselI}\left (-\frac {3}{4}, 2\right ) x +\operatorname {BesselK}\left (\frac {3}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselI}\left (\frac {1}{4}, 2\right ) \textit {\_Z} +2 \operatorname {BesselK}\left (\frac {3}{4}, \frac {\textit {\_Z}^{2}}{2}\right ) \operatorname {BesselI}\left (-\frac {3}{4}, 2\right ) \textit {\_Z} \right ) \]

✗ Mathematica

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

RecursionError : maximum recursion depth exceeded