63.5.3 problem 1(c)

Internal problem ID [13077]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:34 AM
CAS classification : [[_Riccati, _special]]

\begin{align*} x^{\prime }&=t -x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.133 (sec). Leaf size: 223

DSolve[D[x[t],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*}