58.2.41 problem 41
Internal
problem
ID
[9164]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
41
Date
solved
:
Sunday, March 30, 2025 at 02:24:33 PM
CAS
classification
:
[[_Riccati, _special]]
\begin{align*} y^{\prime }&=x -y^{2} \end{align*}
✓ Maple. Time used: 0.001 (sec). Leaf size: 23
ode:=diff(y(x),x) = x-y(x)^2;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {c_1 \operatorname {AiryAi}\left (1, x\right )+\operatorname {AiryBi}\left (1, x\right )}{c_1 \operatorname {AiryAi}\left (x \right )+\operatorname {AiryBi}\left (x \right )}
\]
✓ Mathematica. Time used: 0.125 (sec). Leaf size: 223
ode=D[y[x],x]==x-y[x]^2;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {-i x^{3/2} \left (2 \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i x^{3/2}\right )+c_1 \left (\operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i x^{3/2}\right )-\operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i x^{3/2}\right )\right )\right )-c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )}{2 x \left (\operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i x^{3/2}\right )+c_1 \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i x^{3/2}\right )\right )} \\
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 )} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x + y(x)**2 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
TypeError : bad operand type for unary -: list