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]]
Solve \begin {gather*} \boxed {y^{\prime }-t^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(diff(y(t),t)=t^2+y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (-\BesselJ \left (-\frac {3}{4}, \frac {t^{2}}{2}\right ) c_{1}-\BesselY \left (-\frac {3}{4}, \frac {t^{2}}{2}\right )\right ) t}{c_{1} \BesselJ \left (\frac {1}{4}, \frac {t^{2}}{2}\right )+\BesselY \left (\frac {1}{4}, \frac {t^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 93
DSolve[y'[t]==t^2+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t \left (-J_{-\frac {3}{4}}\left (\frac {t^2}{2}\right )+c_1 J_{\frac {3}{4}}\left (\frac {t^2}{2}\right )\right )}{J_{\frac {1}{4}}\left (\frac {t^2}{2}\right )+c_1 J_{-\frac {1}{4}}\left (\frac {t^2}{2}\right )} \\ y(t)\to \frac {t J_{\frac {3}{4}}\left (\frac {t^2}{2}\right )}{J_{-\frac {1}{4}}\left (\frac {t^2}{2}\right )} \\ \end{align*}