29.3.8 problem 62

Internal problem ID [4670]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 62
Date solved : Sunday, March 30, 2025 at 03:35:45 AM
CAS classification : [_Riccati]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==f[x]+g[x] y[x]+a y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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