Internal problem ID [1699]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-y^{2}=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(t),t)= t+y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {c_{1} \operatorname {AiryAi}\left (1, -t \right )+\operatorname {AiryBi}\left (1, -t \right )}{c_{1} \operatorname {AiryAi}\left (-t \right )+\operatorname {AiryBi}\left (-t \right )} \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 195
DSolve[y'[t]== t+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t^{3/2} \left (-2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 t^{3/2}}{3}\right )+c_1 \left (\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 t^{3/2}}{3}\right )-\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 t^{3/2}}{3}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 t^{3/2}}{3}\right )}{2 t \left (\operatorname {BesselJ}\left (\frac {1}{3},\frac {2 t^{3/2}}{3}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 t^{3/2}}{3}\right )\right )} \\ 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 )} \\ \end{align*}