71.3.10 problem 5 (J)

Internal problem ID [14289]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 5 (J)
Date solved : Monday, March 31, 2025 at 12:15:39 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 45

ode:=diff(y(x),x) = y(x)^2-x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 196

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

\begin{align*} y(x)\to -\frac {i x^2 \left (2 \operatorname {BesselJ}\left (-\frac {3}{4},\frac {i x^2}{2}\right )+c_1 \left (\operatorname {BesselJ}\left (-\frac {5}{4},\frac {i x^2}{2}\right )-\operatorname {BesselJ}\left (\frac {3}{4},\frac {i x^2}{2}\right )\right )\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {i x^2}{2}\right )}{2 x \left (\operatorname {BesselJ}\left (\frac {1}{4},\frac {i x^2}{2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {i x^2}{2}\right )\right )} \\ y(x)\to -\frac {i x^2 \operatorname {BesselJ}\left (-\frac {5}{4},\frac {i x^2}{2}\right )-i x^2 \operatorname {BesselJ}\left (\frac {3}{4},\frac {i x^2}{2}\right )+\operatorname {BesselJ}\left (-\frac {1}{4},\frac {i x^2}{2}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{4},\frac {i x^2}{2}\right )} \\ \end{align*}

✗ Sympy

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

TypeError : bad operand type for unary -: list