66.1.22 problem Problem 30

Internal problem ID [13869]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 30
Date solved : Tuesday, January 28, 2025 at 06:06:17 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 35

dsolve([diff(y(x),x)=x+y(x)^2,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: 1.239 (sec). Leaf size: 80

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

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