23.5.114 problem 114

Internal problem ID [6723]
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 : 114
Date solved : Friday, October 03, 2025 at 02:09:49 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -8 y+3 \left (1+x \right ) y^{\prime }+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=-8*y(x)+3*(1+x)*diff(y(x),x)+(1+x)^2*diff(diff(y(x),x),x)+(1+x)^3*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (1+x \right )^{2}+c_2 \sin \left (2 \ln \left (1+x \right )\right )+c_3 \cos \left (2 \ln \left (1+x \right )\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 34

ode=-8*y[x] + 3*(1 + x)*D[y[x],x] + (1 + x)^2*D[y[x],{x,2}] + (1 + x)^3*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 (x+1)^2+c_1 \cos (2 \log (x+1))+c_2 \sin (2 \log (x+1)) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**3*Derivative(y(x), (x, 3)) + (x + 1)**2*Derivative(y(x), (x, 2)) + (3*x + 3)*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*Derivative(y(x), (x, 3)) - x**2*Der