13.5.3 problem 6

Internal problem ID [2349]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.10. Page 80
Problem number : 6
Date solved : Saturday, March 29, 2025 at 11:58:21 PM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

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

✓ Maple. Time used: 0.167 (sec). Leaf size: 35

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

\[ y = \frac {\sqrt {3}\, \operatorname {AiryAi}\left (1, -t \right )+\operatorname {AiryBi}\left (1, -t \right )}{\sqrt {3}\, \operatorname {AiryAi}\left (-t \right )+\operatorname {AiryBi}\left (-t \right )} \]

✓ Mathematica. Time used: 1.041 (sec). Leaf size: 80

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 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