66.3.2 problem 2

Internal problem ID [15953]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:32:48 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.202 (sec). Leaf size: 89

ode:=diff(y(t),t) = t-y(t)^2; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {-2 \operatorname {AiryAi}\left (1, t\right ) \pi 3^{{5}/{6}}+3 \Gamma \left (\frac {2}{3}\right )^{2} \operatorname {AiryAi}\left (1, t\right ) 3^{{2}/{3}}+3 \Gamma \left (\frac {2}{3}\right )^{2} \operatorname {AiryBi}\left (1, t\right ) 3^{{1}/{6}}+2 \operatorname {AiryBi}\left (1, t\right ) \pi 3^{{1}/{3}}}{-2 \operatorname {AiryAi}\left (t \right ) \pi 3^{{5}/{6}}+3 \Gamma \left (\frac {2}{3}\right )^{2} \operatorname {AiryAi}\left (t \right ) 3^{{2}/{3}}+3 \Gamma \left (\frac {2}{3}\right )^{2} \operatorname {AiryBi}\left (t \right ) 3^{{1}/{6}}+2 \operatorname {AiryBi}\left (t \right ) \pi 3^{{1}/{3}}} \]

✓ Mathematica. Time used: 8.061 (sec). Leaf size: 163

ode=D[y[t],t]==t-y[t]^2; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {2 i t^{3/2} \operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+\sqrt [3]{-3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \left (i t^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i t^{3/2}\right )-i t^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )\right )}{2 t \left (\sqrt [3]{-3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )+\operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i t^{3/2}\right )\right )} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t + y(t)**2 + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

TypeError : bad operand type for unary -: list