20.4.43 problem Problem 61

Internal problem ID [3678]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 61
Date solved : Sunday, March 30, 2025 at 02:04:56 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \end{align*}

✗ Maple

ode:=diff(y(x),x)+p(x)*y(x)+q(x)*y(x)^2 = r(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]+p[x]*y[x]+q[x]*y[x]^2==r[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE p(x)*y(x) + q(x)*y(x)**2 - r(x) + Derivative(y(x), x) cannot be solved by the lie group method