73.15.28 problem 22.10 (a)

Internal problem ID [15459]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (a)
Date solved : Tuesday, January 28, 2025 at 07:56:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=(72*x^2-1)*exp(2*x),y(x), singsol=all)
 

\[ y = \left (-6 x^{2}-x -1\right ) {\mathrm e}^{-2 x} {\mathrm e}^{4 x}+\left ({\mathrm e}^{7 x} c_{2} +c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==(72*x^2-1)*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^{2 x} \left (6 x^2+x+1\right )+c_1 e^{-2 x}+c_2 e^{5 x} \]