55.24.51 problem 51

Internal problem ID [13680]
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 : 51
Date solved : Sunday, October 12, 2025 at 04:26:55 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 190

ode:=y(x)*diff(y(x),x)-1/5*a*(x+4)/x^(8/5)*y(x) = 1/5*a^2*(x-1)*(3*x+7)/x^(11/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\frac {360 \sqrt {17}\, 2^{{1}/{3}} \sqrt {-\frac {\left (x -1\right ) a +y x^{{3}/{5}}}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}}\, 91^{{5}/{6}} \left (x -\frac {21}{4}\right ) \left (\frac {\left (3 x +7\right ) a +3 y x^{{3}/{5}}}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{7}/{6}}}{4444531}[phone] \left (\int _{}^{-\frac {315 \left (4 y x^{{3}/{5}}+4 a x -21 a \right )}{884 \left (y x^{{3}/{5}}+a x \right )}}\frac {\left (68 \textit {\_a} +315\right )^{{1}/{6}} \sqrt {52 \textit {\_a} -315}\, \textit {\_a}}{\left (11492 \textit {\_a}^{2}-53235 \textit {\_a} -99225\right ) \left (221 \textit {\_a} +315\right )^{{5}/{3}}}d \textit {\_a} +\frac {c_1}{31255875}\right ) \left (\frac {a}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{5}/{3}} x}{\left (\frac {a}{x^{{3}/{5}} \left (y+a \,x^{{2}/{5}}\right )}\right )^{{5}/{3}} x} = 0 \]

✗ Mathematica

ode=y[x]*D[y[x],x]-1/5*a*(x+4)*x^(-8/5)*y[x]==1/5*a^2*(x-1)*(3*x+7)*x^(-11/5); 
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)*(3*x + 7)/(5*x**(11/5)) - a*(x + 4)*y(x)/(5*x**(8/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out