29.15.14 problem 422

Internal problem ID [5020]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 422
Date solved : Sunday, March 30, 2025 at 06:30:15 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE f(x)/y(x) - g(x) + Derivative(y(x), x) cannot be solved by the factorable group method