Internal problem ID [12972]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 3. Some basics about First order equations. Additional exercises. page
63
Problem number: 3.4 e.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-y^{2}=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)-y(x)^2=x,y(x), singsol=all)
\[ y = \frac {c_{1} \operatorname {AiryAi}\left (1, -x \right )+\operatorname {AiryBi}\left (1, -x \right )}{c_{1} \operatorname {AiryAi}\left (-x \right )+\operatorname {AiryBi}\left (-x \right )} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 195
DSolve[y'[x]-y[x]^2==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{3/2} \left (-2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 x^{3/2}}{3}\right )+c_1 \left (\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 x^{3/2}}{3}\right )-\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 x^{3/2}}{3}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \left (\operatorname {BesselJ}\left (\frac {1}{3},\frac {2 x^{3/2}}{3}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )\right )} y(x)\to -\frac {x^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 x^{3/2}}{3}\right )-x^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2 x^{3/2}}{3}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )} \end{align*}