23.5.182 problem 182

Internal problem ID [6791]
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 : 182
Date solved : Tuesday, September 30, 2025 at 03:51:43 PM
CAS classification : [[_high_order, _fully, _exact, _linear]]

\begin{align*} {\mathrm e}^{x} y+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left (2+{\mathrm e}^{x}\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=exp(x)*y(x)+4*exp(x)*diff(y(x),x)+6*exp(x)*diff(diff(y(x),x),x)+4*(2+exp(x))*diff(diff(diff(y(x),x),x),x)+(exp(x)+2*x)*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}+c_2 \,x^{2}+c_3 x +c_4}{{\mathrm e}^{x}+2 x} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 32

ode=E^x*y[x] + 4*E^x*D[y[x],x] + 6*E^x*D[y[x],{x,2}] + 4*(2 + E^x)*D[y[x],{x,3}] + (E^x + 2*x)*D[y[x],{x,4}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x (x (c_4 x+c_3)+c_2)+c_1}{2 x+e^x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x + exp(x))*Derivative(y(x), (x, 4)) + (4*exp(x) + 8)*Derivative(y(x), (x, 3)) + y(x)*exp(x) + 4*exp(x)*Derivative(y(x), x) + 6*exp(x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-2*x*Derivative(y(x), (x, 4)) + (-y(x) - 6*Derivative(y(x), (x