Internal problem ID [11411]
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 1.4.1. Integrating factors. Exercises
page 41
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {x^{\prime }+x^{2}=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(x(t),t)=t-x(t)^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {c_{1} \operatorname {AiryAi}\left (1, t\right )+\operatorname {AiryBi}\left (1, t\right )}{c_{1} \operatorname {AiryAi}\left (t \right )+\operatorname {AiryBi}\left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 223
DSolve[x'[t]==t-x[t]^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {-i t^{3/2} \left (2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+c_1 \left (\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i t^{3/2}\right )-\operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i t^{3/2}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )}{2 t \left (\operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i t^{3/2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )\right )} x(t)\to \frac {i t^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i t^{3/2}\right )-i t^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )}{2 t \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )} \end{align*}