14.4.6 problem 6

Internal problem ID [2524]
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 : 6
Date solved : Sunday, March 30, 2025 at 12:08:23 AM
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: 0.161 (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: 0.002 (sec). Leaf size: 6

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

\[ y(t)\to 0 \]

✗ 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