2.24.38 Problem 55
Internal
problem
ID
[13602]
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
:
55
Date
solved
:
Friday, December 19, 2025 at 08:10:55 AM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class B`]]
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*}
Unknown ode type.
2.24.38.1 ✗ Maple
ode:=y(x)*diff(y(x),x)-3*a/x^(7/4)*y(x) = 1/4*a^2*(x-1)*(x-9)/x^(5/2);
dsolve(ode,y(x), singsol=all);
\[ \text {No solution found} \]
Maple step by step
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & y \left (x \right ) \left (\frac {d}{d x}y \left (x \right )\right )-\frac {3 a y \left (x \right )}{x^{{7}/{4}}}=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & \frac {d}{d x}y \left (x \right ) \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & \frac {d}{d x}y \left (x \right )=\frac {\frac {3 a y \left (x \right )}{x^{{7}/{4}}}+\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}}}{y \left (x \right )} \end {array} \]
2.24.38.2 ✗ Mathematica
ode=y[x]*D[y[x],x]-3*a*x^(-7/4)*y[x]==1/4*a^2*(x-1)*(x-9)*x^(-5/2);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Not solved
2.24.38.3 ✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
y = Function("y")
ode = Eq(-a**2*(x - 9)*(x - 1)/(4*x**(5/2)) - 3*a*y(x)/x**(7/4) + y(x)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out