61.24.3 problem 3

Internal problem ID [12337]
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 : 3
Date solved : Monday, March 31, 2025 at 05:11:07 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 4589

ode:=2*y(x)*diff(y(x),x) = (7*a*x+5*b)*y(x)-3*a^2*x^3-2*c*x^2-3*b^2*x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=2*y[x]*D[y[x],x]==(7*a*x+5*b)*y[x]-3*a^2*x^3-2*c*x^2-3*b^2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(3*a**2*x**3 + 3*b**2*x + 2*c*x**2 - (7*a*x + 5*b)*y(x) + 2*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out