73.16.5 problem 24.1 (e)

Internal problem ID [15517]
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 : Tuesday, January 28, 2025 at 08:00:50 AM
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*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 22

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

\[ y = {\mathrm e}^{2 x} \left (2 x^{4}+c_{1} x +x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

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

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

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