54.4.28 problem 1484

Internal problem ID [12750]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1484
Date solved : Wednesday, October 01, 2025 at 02:21:35 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \end{align*}

✗ Maple

ode:=2*x*diff(diff(diff(y(x),x),x),x)+3*(2*a*x+k)*diff(diff(y(x),x),x)+6*(a*k+b*x)*diff(y(x),x)+(3*b*k+2*c*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(3*b*k + 2*c*x)*y[x] + 6*(a*k + b*x)*D[y[x],x] + 3*(k + 2*a*x)*D[y[x],{x,2}] + 2*x*Derivative[3][y][x] == 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") 
c = symbols("c") 
k = symbols("k") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), (x, 3)) + (6*a*k + 6*b*x)*Derivative(y(x), x) + (6*a*x + 3*k)*Derivative(y(x), (x, 2)) + (3*b*k + 2*c*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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