55.24.2 problem 2

Internal problem ID [13631]
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 : 2
Date solved : Wednesday, October 01, 2025 at 07:48:15 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }&=\left (3 a x +b \right ) y-a^{2} x^{3}-a \,x^{2} b +c x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 826

ode:=y(x)*diff(y(x),x) = (3*a*x+b)*y(x)-a^2*x^3-a*b*x^2+c*x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 2.95 (sec). Leaf size: 194

ode=y[x]*D[y[x],x]==(3*a*x+b)*y[x]-a^2*x^3-a*b*x^2+c*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2 a b \left (\text {RootSum}\left [\text {$\#$1}^4 a^2+\text {$\#$1}^3 a b-2 \text {$\#$1}^2 a y(x)-\text {$\#$1}^2 c-\text {$\#$1} b y(x)+y(x)^2\&,\frac {-2 \text {$\#$1}^3 a^2 \log (x-\text {$\#$1})-\text {$\#$1}^2 a b \log (x-\text {$\#$1})+2 \text {$\#$1} a y(x) \log (x-\text {$\#$1})+b y(x) \log (x-\text {$\#$1})+\text {$\#$1} c \log (x-\text {$\#$1})}{-4 \text {$\#$1}^3 a^2-3 \text {$\#$1}^2 a b+4 \text {$\#$1} a y(x)+2 \text {$\#$1} c+b y(x)}\&\right ]-\log \left (a \left (-a x^2-b x+y(x)\right )+c\right )\right )}{c (3 a+b+c-1)}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(a**2*x**3 + a*b*x**2 - c*x - (3*a*x + b)*y(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out