61.24.45 problem 45

Internal problem ID [12379]
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 : 45
Date solved : Monday, March 31, 2025 at 05:23:25 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{{22}/{15}}}&=-\frac {a^{2} \left (x -1\right ) \left (x +4\right )}{30 x^{{29}/{15}}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+1/30*a*(17*x+18)/x^(22/15)*y(x) = -1/30*a^2*(x-1)*(x+4)/x^(29/15); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/30*a*(17*x+18)*x^(-22/15)*y[x]==-1/30*a^2*(x-1)*(x+4)*x^(-29/15); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*(x - 1)*(x + 4)/(30*x**(29/15)) + a*(17*x + 18)*y(x)/(30*x**(22/15)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out