29.4.5 problem 92

Internal problem ID [4696]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 92
Date solved : Tuesday, March 04, 2025 at 07:04:36 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=\operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \end{align*}

✗ Maple

ode:=diff(y(x),x) = f0(x)+f1(x)*y(x)+f2(x)*y(x)^2+f3(x)*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==f0[x]+f1[x]y[x]+f2[x] y[x]^2+f3[x]y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
f0 = Function("f0") 
f1 = Function("f1") 
f2 = Function("f2") 
f3 = Function("f3") 
ode = Eq(-f0(x) - f1(x)*y(x) - f2(x)*y(x)**2 - f3(x)*y(x)**3 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -f0(x) - f1(x)*y(x) - f2(x)*y(x)**2 - f3(x)*y(x)**3 + Derivative(y(x), x) cannot be solved by the lie group method