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]]
Solve \begin {gather*} \boxed {y^{\prime }-t -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(diff(y(t),t)= t+y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \AiryAi \left (1, -t \right )+\AiryBi \left (1, -t \right )}{c_{1} \AiryAi \left (-t \right )+\AiryBi \left (-t \right )} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 110
DSolve[y'[t]== t+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt {t} \left (-J_{-\frac {2}{3}}\left (\frac {2 t^{3/2}}{3}\right )+c_1 J_{\frac {2}{3}}\left (\frac {2 t^{3/2}}{3}\right )\right )}{J_{\frac {1}{3}}\left (\frac {2 t^{3/2}}{3}\right )+c_1 J_{-\frac {1}{3}}\left (\frac {2 t^{3/2}}{3}\right )} \\ y(t)\to \frac {t^2 \, _0\tilde {F}_1\left (;\frac {5}{3};-\frac {t^3}{9}\right )}{3 \, _0\tilde {F}_1\left (;\frac {2}{3};-\frac {t^3}{9}\right )} \\ \end{align*}