23.5.33 problem 33

Internal problem ID [6642]
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 : 33
Date solved : Tuesday, September 30, 2025 at 03:50:28 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

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

\[ y = -\left (c_1 x +c_1 +c_2 \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-\frac {5 x^{2}}{2}+8 x +c_3 \]

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{6} x \left (2 x^2-15 x+48\right )-e^{-x} (c_2 (x+1)+c_1)+c_3 \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = C_{1} + \frac {x^{3}}{3} - \frac {5 x^{2}}{2} + 8 x + \left (C_{2} + C_{3} x\right ) e^{- x} \]