60.4.54 problem 1512

Internal problem ID [11477]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1512
Date solved : Wednesday, March 05, 2025 at 02:26:31 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+(-a^2+1)*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} +c_{2} x^{a}+c_3 \,x^{-a} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 29

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

\[ y(x)\to \frac {-c_1 x^{-a}+c_2 x^a+a c_3}{a} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) + x*(1 - a**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x*(x*Derivative(y(x), (x, 3)) + 3*Derivative(y(x), (x, 2)))/(a**2 - 1) + Derivative(y(x), x) cannot be solved by the factorable group method