66.1.28 problem Problem 40
Internal
problem
ID
[13875]
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
Date
solved
:
Tuesday, January 28, 2025 at 06:06:39 AM
CAS
classification
:
[[_Riccati, _special]]
\begin{align*} y^{\prime }&=x -y^{2} \end{align*}
With initial conditions
\begin{align*} y \left (1\right )&=0 \end{align*}
✓ Solution by Maple
Time used: 0.207 (sec). Leaf size: 37
dsolve([diff(y(x),x)=x-y(x)^2,y(1) = 0],y(x), singsol=all)
\[
y = \frac {\operatorname {AiryBi}\left (1, 1\right ) \operatorname {AiryAi}\left (1, x\right )-\operatorname {AiryBi}\left (1, x\right ) \operatorname {AiryAi}\left (1, 1\right )}{\operatorname {AiryBi}\left (1, 1\right ) \operatorname {AiryAi}\left (x \right )-\operatorname {AiryBi}\left (x \right ) \operatorname {AiryAi}\left (1, 1\right )}
\]
✓ Solution by Mathematica
Time used: 0.150 (sec). Leaf size: 229
DSolve[{D[y[x],x]==x-y[x]^2,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to \frac {i \left (x^{3/2} \left (-\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 i}{3}\right )+i \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 i}{3}\right )+\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 i}{3}\right )\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i x^{3/2}\right )+x^{3/2} \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i x^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 i}{3}\right ) \left (x^{3/2} \left (-\operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i x^{3/2}\right )\right )-i \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )\right )\right )}{x \left (2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2 i}{3}\right ) \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )+\left (-\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 i}{3}\right )+i \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 i}{3}\right )+\operatorname {BesselJ}\left (\frac {2}{3},\frac {2 i}{3}\right )\right ) \operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i x^{3/2}\right )\right )}
\]