85.57.1 problem 1

Internal problem ID [22836]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 200
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:15:34 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=x^{2} {\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 40

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)-2*diff(y(x),x)+24*y(x) = x^2*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x \left (25 x^{2}+60 x +126\right ) {\mathrm e}^{3 x}}{375}+c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 49

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]-2*D[y[x],{x,1}]+24*y[x]==x^2*exp(3*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\exp \left (288 x^3+72 x^2+372 x-11\right )}{2304}+c_1 e^{-2 x}+e^{3 x} \left (c_3 e^x+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.264 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*exp(3*x) + 24*y(x) - 2*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- 2 x} + C_{3} e^{4 x} + \left (C_{1} - \frac {x^{3}}{15} - \frac {4 x^{2}}{25} - \frac {42 x}{125}\right ) e^{3 x} \]