83.30.10 problem 10

Internal problem ID [19310]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 10
Date solved : Thursday, March 13, 2025 at 02:13:30 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 27

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

\[ y \left (x \right ) = c_{1} +c_{2} \left (x -1\right ) {\mathrm e}^{x}+c_3 \left (\int \left (-\operatorname {Ei}_{1}\left (x \right ) x \,{\mathrm e}^{x}+1\right )d x \right ) \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 39

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

\[ y(x)\to -c_2 e^x (x-1) \operatorname {ExpIntegralEi}(-x)+c_1 e^x (x-1)-c_2 \log (-x)+c_3 \]

✗ Sympy

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

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