14.4.16 problem 16

Internal problem ID [2534]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 16
Date solved : Sunday, March 30, 2025 at 12:09:08 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.270 (sec). Leaf size: 43

ode:=diff(y(t),t) = t^2+y(t)^2; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.326 (sec). Leaf size: 68

ode=D[y[t],t]==t^2+y[t]^2; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {t^2 \operatorname {BesselJ}\left (-\frac {5}{4},\frac {t^2}{2}\right )-t^2 \operatorname {BesselJ}\left (\frac {3}{4},\frac {t^2}{2}\right )+\operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )}{2 t \operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )} \]

✗ Sympy

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

TypeError : bad operand type for unary -: list