73.16.5 problem 24.1 (e)

Internal problem ID [15446]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (e)
Date solved : Monday, March 31, 2025 at 01:38:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

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

\[ y = {\mathrm e}^{2 x} \left (2 x^{4}+c_1 x +x^{2}+c_2 \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 26

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

\[ y(x)\to e^{2 x} \left (2 x^4+x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.298 (sec). Leaf size: 19

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

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