Internal problem ID [14438]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-y^{2}=-x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 28
dsolve([diff(y(x),x)=y(x)^2-x,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\sqrt {3}\, \operatorname {AiryAi}\left (1, x\right )-\operatorname {AiryBi}\left (1, x\right )}{\sqrt {3}\, \operatorname {AiryAi}\left (x \right )+\operatorname {AiryBi}\left (x \right )} \]
✓ Solution by Mathematica
Time used: 6.859 (sec). Leaf size: 93
DSolve[{y'[x]==y[x]^2-x,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {i x^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i x^{3/2}\right )-i x^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i x^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )} \]