54.1.142 problem 145
Internal
problem
ID
[11456]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
145
Date
solved
:
Sunday, October 12, 2025 at 01:38:10 AM
CAS
classification
:
[_rational, _Abel]
\begin{align*} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 148
ode:=x^2*diff(y(x),x)+a*y(x)^3-a*x^2*y(x)^2 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {1}{a x +2^{{2}/{3}} \left (-a \right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right ) c_1 \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right )+\operatorname {AiryBi}\left (1, \frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right ) c_1 +\operatorname {AiryAi}\left (1, \frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right )\right )}
\]
✓ Mathematica. Time used: 8.715 (sec). Leaf size: 303
ode=x^2*D[y[x],x] + a*y[x]^3 - a*x^2*y[x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\frac {\left (-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x\right ) \operatorname {AiryAi}\left (\left (-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}\right )^2-\frac {\sqrt [3]{-\frac {1}{2}}}{\sqrt [3]{a} x}\right )+\operatorname {AiryAiPrime}\left (\left (-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}\right )^2-\frac {\sqrt [3]{-\frac {1}{2}}}{\sqrt [3]{a} x}\right )}{\left (-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x\right ) \operatorname {AiryBi}\left (\left (-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}\right )^2-\frac {\sqrt [3]{-\frac {1}{2}}}{\sqrt [3]{a} x}\right )+\operatorname {AiryBiPrime}\left (\left (-\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{a} x-\frac {\left (-\frac {1}{2}\right )^{2/3}}{a^{2/3} y(x)}\right )^2-\frac {\sqrt [3]{-\frac {1}{2}}}{\sqrt [3]{a} x}\right )}+c_1=0,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
y = Function("y")
ode = Eq(-a*x**2*y(x)**2 + a*y(x)**3 + x**2*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
RecursionError : maximum recursion depth exceeded