Internal problem ID [10383]
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]]
\[ \boxed {x^{\prime }-t +x^{2}=0} \]
✓ 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: 0.157 (sec). Leaf size: 118
DSolve[x'[t]==t-x[t]^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {i \sqrt {t} \left (\operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i t^{3/2}\right )-c_1 \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i t^{3/2}\right )\right )}{\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 )} \\ x(t)\to \frac {3 \operatorname {AiryAiPrime}(t)+\sqrt {3} \operatorname {AiryBiPrime}(t)}{3 \operatorname {AiryAi}(t)+\sqrt {3} \operatorname {AiryBi}(t)} \\ \end{align*}