23.5.74 problem 74

Internal problem ID [6683]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 74
Date solved : Friday, October 03, 2025 at 02:09:43 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

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

\[ y = c_1 x +c_2 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to c_1 x-c_2 \cosh (x)+i c_3 \sinh (x) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x*Derivative(y(x), (x, 3)) + y(x) - Deriv