Internal problem ID [10791]
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 40.
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 (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 37
dsolve([diff(y(x),x)=x-y(x)^2,y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {AiryBi}\left (1, 1\right ) \operatorname {AiryAi}\left (1, x\right )-\operatorname {AiryBi}\left (1, x\right ) \operatorname {AiryAi}\left (1, 1\right )}{\operatorname {AiryBi}\left (1, 1\right ) \operatorname {AiryAi}\left (x \right )-\operatorname {AiryBi}\left (x \right ) \operatorname {AiryAi}\left (1, 1\right )} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 119
DSolve[{y'[x]==x-y[x]^2,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \sqrt {x} \left (\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i x^{3/2}\right )-\operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i x^{3/2}\right )\right )}{\operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )+\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i x^{3/2}\right )} \\ \end{align*}