Internal problem ID [10785]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }-x -y^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve([diff(y(x),x)=x+y(x)^2,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: 1.248 (sec). Leaf size: 36
DSolve[{y'[x]==x+y[x]^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \, _0\tilde {F}_1\left (;\frac {5}{3};-\frac {x^3}{9}\right )}{3 \, _0\tilde {F}_1\left (;\frac {2}{3};-\frac {x^3}{9}\right )} \\ \end{align*}