60.4.21 problem 1477

Internal problem ID [11444]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1477
Date solved : Sunday, March 30, 2025 at 08:22:21 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime \prime }+3 y^{\prime \prime }+x y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=x*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,{\mathrm e}^{-x}+{\mathrm e}^{\frac {x}{2}} \left (c_2 \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \cos \left (\frac {\sqrt {3}\, x}{2}\right )\right )}{x} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 47

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

\[ y(x)\to \frac {c_1 e^{-x-1}+c_2 e^{\sqrt [3]{-1} x}+c_3 e^{-(-1)^{2/3} x-1}}{x} \]

✗ Sympy

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

NotImplementedError : solve: Cannot solve x*y(x) + x*Derivative(y(x), (x, 3)) + 3*Derivative(y(x), (x, 2))