90.3.8 problem 8

Internal problem ID [25072]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 8
Date solved : Thursday, October 02, 2025 at 11:48:22 PM
CAS classification : [[_Riccati, _special]]

\begin{align*} y^{\prime }&=t^{2}+y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 43

ode:=diff(y(t),t) = t^2+y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 169

ode=D[y[t],{t,1}]==t^2+y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

TypeError : bad operand type for unary -: list