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
:
Tuesday, January 28, 2025 at 02:39:58 PM
CAS
classification
:
[_rational, _Abel]
\begin{align*} x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \end{align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 178
dsolve(x^2*diff(y(x),x)+a*y(x)^2+b*x^2*y(x)^3 = 0,y(x), singsol=all)
\[
y \left (x \right ) = -\frac {2^{{1}/{3}} a b x}{2^{{1}/{3}} a^{2} b -2 \left (a^{2} b^{2}\right )^{{2}/{3}} \operatorname {RootOf}\left (\operatorname {AiryBi}\left (-\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \operatorname {AiryAi}\left (-\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )+\operatorname {AiryBi}\left (1, -\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right ) c_{1} +\operatorname {AiryAi}\left (1, -\frac {b 2^{{2}/{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{{1}/{3}}}{2 \left (a^{2} b^{2}\right )^{{1}/{3}}}\right )\right ) x}
\]
✓ Solution by Mathematica
Time used: 0.588 (sec). Leaf size: 343
DSolve[x^2 D[y[x],x]+a y[x]^2+b x^2 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\frac {\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryAi}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\operatorname {AiryAiPrime}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}{\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {AiryBi}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\operatorname {AiryBiPrime}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}+c_1=0,y(x)\right ]
\]