Internal problem ID [1709]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-y^{2}=t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(t),t)=t^2+y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-\operatorname {BesselJ}\left (-\frac {3}{4}, \frac {t^{2}}{2}\right ) c_{1} -\operatorname {BesselY}\left (-\frac {3}{4}, \frac {t^{2}}{2}\right )\right ) t}{c_{1} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )+\operatorname {BesselY}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 169
DSolve[y'[t]==t^2+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t^2 \left (-2 \operatorname {BesselJ}\left (-\frac {3}{4},\frac {t^2}{2}\right )+c_1 \left (\operatorname {BesselJ}\left (\frac {3}{4},\frac {t^2}{2}\right )-\operatorname {BesselJ}\left (-\frac {5}{4},\frac {t^2}{2}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )}{2 t \left (\operatorname {BesselJ}\left (\frac {1}{4},\frac {t^2}{2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )\right )} y(t)\to -\frac {t^2 \operatorname {BesselJ}\left (-\frac {5}{4},\frac {t^2}{2}\right )-t^2 \operatorname {BesselJ}\left (\frac {3}{4},\frac {t^2}{2}\right )+\operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )}{2 t \operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )} \end{align*}