76.33.16 problem Ex. 16

Internal problem ID [20194]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 16
Date solved : Thursday, October 02, 2025 at 05:34:07 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

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

\[ y = \left (c_1 x -2 c_1 +c_2 \right ) {\mathrm e}^{x}+\frac {x^{3}}{6}+x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 37

ode=D[y[x],{x,4}]-2*D[y[x],{x,3}]+D[y[x],{x,2}]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3}{6}+x^2+c_4 x+c_1 e^x+c_2 e^x (x-2)+c_3 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} + C_{4} e^{x} + \frac {x^{3}}{6} + x^{2} + x \left (C_{2} + C_{3} e^{x}\right ) \]