73.17.33 problem 33

Internal problem ID [15496]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 33
Date solved : Monday, March 31, 2025 at 01:39:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+14*y(x) = 576*x^2*exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_2 +{\mathrm e}^{7 x} c_1 +\frac {\left (288 x^{2}+264 x +97\right ) {\mathrm e}^{-x}}{12} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 39

ode=D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==576*x^2*Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (24 x^2+22 x+c_1 e^{3 x}+c_2 e^{8 x}+\frac {97}{12}\right ) \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-576*x**2*exp(-x) + 14*y(x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{2 x} + C_{2} e^{7 x} + 24 x^{2} e^{- x} + 22 x e^{- x} + \frac {97 e^{- x}}{12} \]