61.22.23 problem 23
Internal
problem
ID
[12348]
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
1.3.1-2.
Solvable
equations
and
their
solutions
Problem
number
:
23
Date
solved
:
Tuesday, January 28, 2025 at 07:55:13 PM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} y^{\prime } y-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \end{align*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 581
dsolve(y(x)*diff(y(x),x)-y(x)=-9/100*x+A*x^(-5/3),y(x), singsol=all)
\[
\frac {10460353203000 A \,x^{{44}/{3}}-895371796800000 A \,x^{{35}/{3}} y^{3}+1205308188000000 A \,x^{{32}/{3}} y^{4}-892820880000000 A \,x^{{29}/{3}} y^{5}+165337200000000 A \,x^{{26}/{3}} y^{6}+314928000000000 A \,x^{{23}/{3}} y^{7}-540000000000000 A^{3} x^{{10}/{3}} y^{6}-1215000000000000 A^{4} x^{{8}/{3}} y^{4}+1093500000000000 y^{2} A \left (-\frac {4 y^{8}}{243}+A^{3}+\frac {c_{1}}{18225000000}\right ) x^{{14}/{3}}+2283228000000000 y A \left (\frac {1100 y^{8}}{21141}+A^{3}+\frac {c_{1}}{21141000000}\right ) x^{{17}/{3}}-1930902300000000 A \left (\frac {1400 y^{8}}{8829}+A^{3}+\frac {c_{1}}{119191500000}\right ) x^{{20}/{3}}+204120000000000 y^{4} \left (-\frac {25 y^{8}}{5103}+A^{3}+\frac {c_{1}}{20412000000}\right ) x^{{16}/{3}}+1614006000000000 y^{2} \left (-\frac {110 y^{8}}{3321}+A^{3}+\frac {c_{1}}{59778000000}\right ) x^{{22}/{3}}-2111592240000000 y \left (-\frac {2750 y^{8}}{36207}+A^{3}+\frac {c_{1}}{217242000000}\right ) x^{{25}/{3}}-571536000000000 y^{3} \left (-\frac {25 y^{8}}{1323}+A^{3}+\frac {c_{1}}{20412000000}\right ) x^{{19}/{3}}-23012777046600 x^{{46}/{3}} y^{2}+85232507580000 x^{{43}/{3}} y^{3}-213081268950000 x^{{40}/{3}} y^{4}+378811144800000 x^{{37}/{3}} y^{5}-491051484000000 x^{{34}/{3}} y^{6}+467668080000000 x^{{31}/{3}} y^{7}+3765727153080 x^{{49}/{3}} y+\left (-1702736964000000 A^{2} x^{10}-1458000000000000 A^{5} x^{2}\right ) y^{2}+\left (792059666400000 A^{2} x^{11}-874800000000000 A^{5} x^{3}\right ) y-135000000000000 A^{2} x^{4} y^{8}+1629752400000000 A^{2} x^{9} y^{3}-531441000000000 A^{2} x^{8} y^{4}+52488000000000 A^{2} x^{7} y^{5}-417960000000000 A^{2} x^{6} y^{6}+453600000000000 A^{2} x^{5} y^{7}+583200000000000 A^{3} x^{{13}/{3}} y^{5}-291600000000000 A^{4} x^{{11}/{3}} y^{3}-97629963228000 A \,x^{{41}/{3}} y+395168898780000 A \,x^{{38}/{3}} y^{2}-282429536481 x^{{52}/{3}}-729000000000000 A^{6} x^{{4}/{3}}+\left (-140762777670000 x^{12}+90000 c_{1} x^{4}\right ) A^{2}+\left (-324769500000000 y^{8}+818419140000000 A^{3}+729 c_{1} \right ) x^{{28}/{3}}+1968300000000000 A^{5} x^{4}}{729 x^{{28}/{3}}-9720 x^{{25}/{3}} y+27000 x^{{22}/{3}} y^{2}-28000 x^{{19}/{3}} y^{3}+10000 x^{{16}/{3}} y^{4}-16200 A \,x^{{20}/{3}}+108000 A \,x^{{17}/{3}} y+60000 A \,x^{{14}/{3}} y^{2}+90000 A^{2} x^{4}} = 0
\]
✓ Solution by Mathematica
Time used: 60.335 (sec). Leaf size: 7909
DSolve[y[x]*D[y[x],x]-y[x]==-9/100*x+A*x^(-5/3),y[x],x,IncludeSingularSolutions -> True]
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