60.1.55 problem 56

Internal problem ID [10069]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 56
Date solved : Wednesday, March 05, 2025 at 08:20:45 AM
CAS classification : [NONE]

\begin{align*} y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)-f(x)*y(x)^a-g(x)*y(x)^b = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

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