61.24.28 problem 28
Internal
problem
ID
[12441]
Book
:
Handbook
of
exact
solutions
for
ordinary
differential
equations.
By
Polyanin
and
Zaitsev.
Second
edition
Section
:
Chapter
1,
section
1.3.
Abel
Equations
of
the
Second
Kind.
subsection
1.3.3-2.
Problem
number
:
28
Date
solved
:
Tuesday, January 28, 2025 at 07:58:52 PM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} y^{\prime } y+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \end{align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 669
dsolve(y(x)*diff(y(x),x)+1/10*a*(7*x-12)*x^(-7/5)*y(x)=-1/10*a^2*(x-1)*(x-16)*x^(-9/5),y(x), singsol=all)
\[
\frac {-25 a^{3} \left (\frac {\left (5 \sqrt {x}+x +4\right ) a +y x^{{2}/{5}}}{\sqrt {x}\, a}\right )^{{3}/{2}} \left (a \,x^{{74}/{5}}-a \,x^{{79}/{5}}-2 a \,x^{\frac {143}{10}}+2 a \,x^{\frac {153}{10}}-y x^{{76}/{5}}+2 x^{\frac {147}{10}} y\right ) \left (-\frac {\left (-5 \sqrt {x}+x +4\right ) a +y x^{{2}/{5}}}{\sqrt {x}\, a}\right )^{{3}/{2}}+16384 c_{1} \left (-\frac {21 x^{\frac {157}{10}} y a^{3}}{64}-\frac {81 x^{\frac {147}{10}} y a^{3}}{256}-\frac {9 y^{2} x^{\frac {151}{10}} a^{2}}{256}+\frac {3 x^{\frac {161}{10}} y^{2} a^{2}}{64}+\frac {x^{{31}/{2}} y^{3} a}{32}+\frac {11 x^{{29}/{2}} y^{3} a}{128}-\frac {\left (-\frac {9 x^{{73}/{5}} y^{2} a}{2}+6 x^{{78}/{5}} y^{2} a +4 x^{{81}/{5}} y a^{2}+x^{{84}/{5}} a^{3}+4 y^{3} \left (x +\frac {11}{4}\right ) x^{14}\right ) a}{64}+\frac {x^{\frac {137}{10}} y a^{3}}{8}+\frac {x^{\frac {167}{10}} y a^{3}}{32}+\frac {9 y^{2} x^{\frac {141}{10}} a^{2}}{32}-\frac {x^{{66}/{5}} y a^{3}}{4}-\frac {9 x^{{68}/{5}} y^{2} a^{2}}{16}+\frac {x^{\frac {149}{10}} y^{4}}{128}+\frac {21 y x^{{76}/{5}} a^{3}}{32}+\frac {81 y x^{{71}/{5}} a^{3}}{128}-\frac {x^{{72}/{5}} y^{4}}{64}-\frac {53 x^{\frac {163}{10}} a^{4}}{256}+\frac {1263 x^{\frac {153}{10}} a^{4}}{1024}+\frac {83 x^{\frac {143}{10}} a^{4}}{64}+\frac {x^{\frac {173}{10}} a^{4}}{128}-\frac {x^{\frac {133}{10}} a^{4}}{2}+x^{{64}/{5}} a^{4}+\frac {53 x^{{79}/{5}} a^{4}}{128}-\frac {1263 x^{{74}/{5}} a^{4}}{512}-\frac {83 x^{{69}/{5}} a^{4}}{32}\right )}{-5376 x^{\frac {157}{10}} y a^{3}-5184 x^{\frac {147}{10}} y a^{3}-576 y^{2} x^{\frac {151}{10}} a^{2}+768 x^{\frac {161}{10}} y^{2} a^{2}+512 x^{{31}/{2}} y^{3} a +1408 x^{{29}/{2}} y^{3} a -256 \left (-\frac {9 x^{{73}/{5}} y^{2} a}{2}+6 x^{{78}/{5}} y^{2} a +4 x^{{81}/{5}} y a^{2}+x^{{84}/{5}} a^{3}+4 y^{3} \left (x +\frac {11}{4}\right ) x^{14}\right ) a +2048 x^{\frac {137}{10}} y a^{3}+512 x^{\frac {167}{10}} y a^{3}+4608 y^{2} x^{\frac {141}{10}} a^{2}-4096 x^{{66}/{5}} y a^{3}-9216 x^{{68}/{5}} y^{2} a^{2}+128 x^{\frac {149}{10}} y^{4}+10752 y x^{{76}/{5}} a^{3}+10368 y x^{{71}/{5}} a^{3}-256 x^{{72}/{5}} y^{4}-3392 x^{\frac {163}{10}} a^{4}+20208 x^{\frac {153}{10}} a^{4}+21248 x^{\frac {143}{10}} a^{4}+128 x^{\frac {173}{10}} a^{4}-8192 x^{\frac {133}{10}} a^{4}+16384 x^{{64}/{5}} a^{4}+6784 x^{{79}/{5}} a^{4}-40416 x^{{74}/{5}} a^{4}-42496 x^{{69}/{5}} a^{4}} = 0
\]
✗ Solution by Mathematica
Time used: 0.000 (sec). Leaf size: 0
DSolve[y[x]*D[y[x],x]+1/10*a*(7*x-12)*x^(-7/5)*y[x]==-1/10*a^2*(x-1)*(x-16)*x^(-9/5),y[x],x,IncludeSingularSolutions -> True]
Timed out