23.1.67 problem 61

Internal problem ID [4674]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 61
Date solved : Tuesday, September 30, 2025 at 07:57:59 AM
CAS classification : [_Riccati]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==f[x]+a*y[x]+b*y[x]^2; 
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") 
f = Function("f") 
ode = Eq(-a*y(x) - b*y(x)**2 - f(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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