61.22.53 problem 53

Internal problem ID [12299]
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 : 53
Date solved : Monday, March 31, 2025 at 05:05:12 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 133

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

\[ \frac {\left (\left (\frac {4 \sqrt {3}\, \left (x -\frac {7 y}{4}\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {7}{6}\right ], \left [\frac {3}{2}\right ], \frac {3 \left (-4 x +7 y\right )^{2}}{196 x^{{3}/{2}} A}\right )}{7}+c_1 \sqrt {x}\, \sqrt {A \sqrt {x}}\right ) 196^{{1}/{6}} \left (\frac {x^{{3}/{2}} A -\frac {12 \left (x -\frac {7 y}{4}\right )^{2}}{49}}{x^{{3}/{2}} A}\right )^{{1}/{6}}-7 \,14^{{1}/{3}} A \sqrt {3}\, \sqrt {x}\right ) 196^{{5}/{6}}}{196 \left (\frac {x^{{3}/{2}} A -\frac {12 \left (x -\frac {7 y}{4}\right )^{2}}{49}}{x^{{3}/{2}} A}\right )^{{1}/{6}} \sqrt {A \sqrt {x}}\, \sqrt {x}} = 0 \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out