Internal problem ID [10341]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.1.3 Geometric. Exercises page
15
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {x^{\prime }-x^{2}-t^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(diff(x(t),t)=x(t)^2+t^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (-\operatorname {BesselJ}\left (-\frac {3}{4}, \frac {t^{2}}{2}\right ) c_{1} -\operatorname {BesselY}\left (-\frac {3}{4}, \frac {t^{2}}{2}\right )\right ) t}{c_{1} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )+\operatorname {BesselY}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 93
DSolve[x'[t]==x[t]^2+t^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {t \left (-\operatorname {BesselJ}\left (-\frac {3}{4},\frac {t^2}{2}\right )+c_1 \operatorname {BesselJ}\left (\frac {3}{4},\frac {t^2}{2}\right )\right )}{\operatorname {BesselJ}\left (\frac {1}{4},\frac {t^2}{2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )} \\ x(t)\to \frac {t \operatorname {BesselJ}\left (\frac {3}{4},\frac {t^2}{2}\right )}{\operatorname {BesselJ}\left (-\frac {1}{4},\frac {t^2}{2}\right )} \\ \end{align*}