29.10.6 problem 272
Internal
problem
ID
[4872]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
10
Problem
number
:
272
Date
solved
:
Tuesday, January 28, 2025 at 02:39:57 PM
CAS
classification
:
[_rational, _Abel]
\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \end{align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 148
dsolve(x^2*diff(y(x),x) = a*x^2*y(x)^2-a*y(x)^3,y(x), singsol=all)
\[
y \left (x \right ) = \frac {1}{-a x -2^{{2}/{3}} \left (-a \right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (\frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right )+\operatorname {AiryBi}\left (1, \frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right ) c_{1} +\operatorname {AiryAi}\left (1, \frac {\left (\textit {\_Z}^{2} 2^{{1}/{3}} \left (-a \right )^{{1}/{3}} x -1\right ) 2^{{2}/{3}}}{2 \left (-a \right )^{{1}/{3}} x}\right )\right )}
\]
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 267
DSolve[x^2 D[y[x],x]==a x^2 y[x]^2-a y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\frac {\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \operatorname {AiryAi}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\operatorname {AiryAiPrime}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}{\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \operatorname {AiryBi}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\operatorname {AiryBiPrime}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}+c_1=0,y(x)\right ]
\]