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 : Monday, January 27, 2025 at 05:49:27 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*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

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

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

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