55.22.24 problem 24

Internal problem ID [13565]
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 : 24
Date solved : Sunday, October 12, 2025 at 03:45:40 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 270

ode:=y(x)*diff(y(x),x)-y(x) = -12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2/x^(1/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (-\sqrt {x}+3 A \right ) \left (36 A^{4}+120 A^{3} \sqrt {x}-80 A \,x^{{3}/{2}}+52 A^{2} x +84 A^{2} y+140 A \sqrt {x}\, y+16 x^{2}-56 x y+49 y^{2}\right ) y}{8 \sqrt {-\frac {\left (-\sqrt {x}+3 A \right )^{2}}{6 A^{2}-2 \sqrt {x}\, A +y}}\, \left (\frac {15 A^{2}+4 \sqrt {x}\, A -3 x +7 y}{6 A^{2}-2 \sqrt {x}\, A +y}\right )^{{3}/{2}} \left (6 A^{2}-2 \sqrt {x}\, A +y\right )^{3} A}+\frac {\left (-54 A^{2}-6 \sqrt {x}\, A +8 x -21 y\right ) \sqrt {-\frac {\left (-\sqrt {x}+3 A \right )^{2}}{6 A^{2}-2 \sqrt {x}\, A +y}}}{\sqrt {\frac {15 A^{2}+4 \sqrt {x}\, A -3 x +7 y}{6 A^{2}-2 \sqrt {x}\, A +y}}\, \left (36 A^{2}-12 \sqrt {x}\, A +6 y\right )}+c_1 = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-y[x]==-12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2*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(-2*A*(15*A**2/sqrt(x) + 34*A + 5*sqrt(x))/49 + 12*x/49 + y(x)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out