29.19.18 problem 531

Internal problem ID [5127]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 531
Date solved : Tuesday, March 04, 2025 at 08:05:42 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✗ Maple

ode:=(a+x*(x+y(x)))*diff(y(x),x) = b*(x+y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(a+x*(x+y[x]))*D[y[x],x]==b*(x+y[x])*y[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") 
y = Function("y") 
ode = Eq(-b*(x + y(x))*y(x) + (a + x*(x + y(x)))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -b*(x + y(x))*y(x)/(a + x**2 + x*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method