85.67.13 problem 13

Internal problem ID [22904]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:16:27 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=12 \,{\mathrm e}^{2 x}+24 x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 44

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+4*diff(y(x),x) = 12*exp(2*x)+24*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (6+12 x^{2}+2 \left (-6+c_1 \right ) x -c_1 +2 c_2 \right ) {\mathrm e}^{2 x}}{4}+2 x^{3}+6 x^{2}+9 x +c_3 \]

✓ Mathematica. Time used: 0.26 (sec). Leaf size: 51

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+4*D[y[x],{x,1}]==12*Exp[2*x]+24*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (2 x^2+6 x+9\right )+\frac {1}{4} e^{2 x} \left (12 x^2+2 (-6+c_2) x+6+2 c_1-c_2\right )+c_3 \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*x**2 - 12*exp(2*x) + 4*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + 2 x^{3} + 6 x^{2} + 9 x + \left (C_{2} + x \left (C_{3} + 3 x\right )\right ) e^{2 x} \]