60.1.144 problem 147
Internal
problem
ID
[10158]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
147
Date
solved
:
Sunday, March 30, 2025 at 03:20:32 PM
CAS
classification
:
[_rational, _Abel]
\begin{align*} x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2}&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 178
ode:=x^2*diff(y(x),x)+a*x^2*y(x)^3+b*y(x)^2 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {2^{{1}/{3}} a b x}{2^{{1}/{3}} a \,b^{2}-2 \left (a^{2} b^{2}\right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (-\frac {a 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_1 \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (-\frac {a 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )+\operatorname {AiryBi}\left (1, -\frac {a 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_1 +\operatorname {AiryAi}\left (1, -\frac {a 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )\right ) x}
\]
✓ Mathematica. Time used: 0.587 (sec). Leaf size: 343
ode=x^2*D[y[x],x] + a*x^2*y[x]^3 + b*y[x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\frac {\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryAi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\operatorname {AiryAiPrime}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}{\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryBi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\operatorname {AiryBiPrime}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}+c_1=0,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(a*x**2*y(x)**3 + b*y(x)**2 + x**2*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE a*y(x)**3 + b*y(x)**2/x**2 + Derivative(y(x), x) cannot be solved by the factorable group method