29.2.28 problem 53
Internal
problem
ID
[4661]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
2
Problem
number
:
53
Date
solved
:
Sunday, March 30, 2025 at 03:34:37 AM
CAS
classification
:
[_Riccati]
\begin{align*} y^{\prime }&=3 a +3 b x +3 b y^{2} \end{align*}
✓ Maple. Time used: 0.010 (sec). Leaf size: 80
ode:=diff(y(x),x) = 3*a+3*b*x+3*b*y(x)^2;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\left (\operatorname {AiryAi}\left (1, -\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right ) c_1 +\operatorname {AiryBi}\left (1, -\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )\right ) 3^{{2}/{3}}}{b^{{1}/{3}} \left (3 c_1 \operatorname {AiryAi}\left (-\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )+3 \operatorname {AiryBi}\left (-\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )\right )}
\]
✓ Mathematica. Time used: 0.216 (sec). Leaf size: 191
ode=D[y[x],x]==3*(a+b*x+ b*y[x]^2);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {b \left (\operatorname {AiryBiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \left (\operatorname {AiryBi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )} \\
y(x)\to \frac {b \operatorname {AiryAiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(-3*a - 3*b*x - 3*b*y(x)**2 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
RecursionError : maximum recursion depth exceeded