60.1.49 problem 50

Internal problem ID [10063]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 50
Date solved : Sunday, March 30, 2025 at 02:58:44 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)-f__3(x)*y(x)^3-f__2(x)*y(x)^2-f__1(x)*y(x)-f__0(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x] - f3[x]*y[x]^3 - f2[x]*y[x]^2 - f1[x]*y[x] - f0[x]==0; 
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