83.11.9 problem 9

Internal problem ID [21998]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 9
Date solved : Thursday, October 02, 2025 at 08:21:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=2 x^{2}-3 x -17 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+3*diff(y(x),x)-y(x) = 2*x^2-3*x-17; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 \,x^{2}+c_2 x +c_1 \right ) {\mathrm e}^{x}-2 x^{2}-9 x +2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 35

ode=D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==2*x^2-3*x-17; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \left (-2+c_3 e^x\right )+x \left (-9+c_2 e^x\right )+c_1 e^x+2 \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**2 + 3*x - y(x) + 3*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + 17,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x^{2} - 9 x + \left (C_{1} + x \left (C_{2} + C_{3} x\right )\right ) e^{x} + 2 \]