29.3.23 problem 77
Internal
problem
ID
[4685]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
3
Problem
number
:
77
Date
solved
:
Tuesday, January 28, 2025 at 02:39:22 PM
CAS
classification
:
[_Abel]
\begin{align*} y^{\prime }+\left (a x +y\right ) y^{2}&=0 \end{align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 71
dsolve(diff(y(x),x)+(a*x+y(x))*y(x)^2=0,y(x), singsol=all)
\[
y \left (x \right ) = \frac {2 a}{a^{2} x^{2}+2 \operatorname {RootOf}\left (2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_{1} x +2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1} +2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right ) 2^{{1}/{3}} \left (-a^{2}\right )^{{1}/{3}}}
\]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 195
DSolve[D[y[x],x]+(a x+y[x])y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\frac {\operatorname {AiryAiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryAi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}{\operatorname {AiryBiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryBi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}+c_1=0,y(x)\right ]
\]