54.4.10 problem 1463

Internal problem ID [12732]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1463
Date solved : Wednesday, October 01, 2025 at 02:21:28 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+2 f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y&=0 \end{align*}

✗ Maple

ode:=diff(diff(diff(y(x),x),x),x)+2*f(x)*diff(y(x),x)+diff(f(x),x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*Derivative[1][f][x] + 2*f[x]*D[y[x],x] + Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(-y(x)*Derivative(f(x), x) - Derivative(y(x), (x, 3)))/(2*f(x)) + Derivative(y(x), x) cannot be solved by the factorable group method