29.10.7 problem 273
Internal
problem
ID
[4873]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
10
Problem
number
:
273
Date
solved
:
Sunday, March 30, 2025 at 04:08:15 AM
CAS
classification
:
[_rational, _Abel]
\begin{align*} x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 178
ode:=x^2*diff(y(x),x)+a*y(x)^2+b*x^2*y(x)^3 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {2^{{1}/{3}} a b x}{2^{{1}/{3}} a^{2} b -2 \left (a^{2} b^{2}\right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (-\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_1 \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (-\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )+\operatorname {AiryBi}\left (1, -\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_1 +\operatorname {AiryAi}\left (1, -\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )\right ) x}
\]
✓ Mathematica. Time used: 0.588 (sec). Leaf size: 343
ode=x^2 D[y[x],x]+a y[x]^2+b x^2 y[x]^3==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\frac {\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryAi}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\operatorname {AiryAiPrime}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}{\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryBi}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\operatorname {AiryBiPrime}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}+c_1=0,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(a*y(x)**2 + b*x**2*y(x)**3 + x**2*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE a*y(x)**2/x**2 + b*y(x)**3 + Derivative(y(x), x) cannot be solved by the factorable group method