61.22.64 problem 64

Internal problem ID [12310]
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 : 64
Date solved : Monday, March 31, 2025 at 05:06:43 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}} \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)-y(x) = -12/49*x+3*A*(1/49+B)*x^(1/2)+3*A^2*(4/49-5/2*B)+15/4*A^3*(1/49-5/4*B)/x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-12/49*x+3*A*(1/49+B)*x^(1/2)+3*A^2*(4/49-5/2*B)+15/4*A^3*(1/49-5/4*B)*x^(-1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
B = symbols("B") 
y = Function("y") 
ode = Eq(-15*A**3*(1/49 - 5*B/4)/(4*sqrt(x)) - 3*A**2*(4/49 - 5*B/2) - 3*A*sqrt(x)*(B + 1/49) + 12*x/49 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out