49.11.5 problem 1(e)

Internal problem ID [7669]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:09:25 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=x^{2} {\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+9*y(x)=x^2*exp(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (x -\frac {1}{3}\right )^{2} {\mathrm e}^{3 x}}{18}+\cos \left (3 x \right ) c_{1} +\sin \left (3 x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]+9*y[x]==x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{162} e^{3 x} (1-3 x)^2+c_1 \cos (3 x)+c_2 \sin (3 x) \]