88.20.11 problem 11

Internal problem ID [24149]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 146
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:00:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=x^{2} {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+8*y(x) = exp(x)*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x} \left (27 c_1 \,{\mathrm e}^{3 x}+54 \,{\mathrm e}^{x} c_2 +18 x^{2}+48 x +52\right )}{54} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 39

ode=D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==x^2*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{27} e^x \left (9 x^2+24 x+26\right )+c_1 e^{2 x}+c_2 e^{4 x} \end{align*}

✓ Sympy. Time used: 0.152 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*exp(x) + 8*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} e^{x} + C_{2} e^{3 x} + \frac {x^{2}}{3} + \frac {8 x}{9} + \frac {26}{27}\right ) e^{x} \]