74.8.36 problem 36

Internal problem ID [16172]
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
Date solved : Tuesday, January 28, 2025 at 08:55:51 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 30

dsolve([diff(y(x),x)=y(x)^2-x,y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {-\sqrt {3}\, \operatorname {AiryAi}\left (1, x\right )-\operatorname {AiryBi}\left (1, x\right )}{\sqrt {3}\, \operatorname {AiryAi}\left (x \right )+\operatorname {AiryBi}\left (x \right )} \]

✓ Solution by Mathematica

Time used: 7.300 (sec). Leaf size: 93

DSolve[{D[y[x],x]==y[x]^2-x,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {i x^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i x^{3/2}\right )-i x^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i x^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )} \]