Internal problem ID [5248]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-x^{2} {\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+9*y(x)=x^2*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {\left (3 x -1\right )^{2} {\mathrm e}^{3 x}}{162} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 36
DSolve[y''[x]+9*y[x]==x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{162} e^{3 x} (1-3 x)^2+c_1 \cos (3 x)+c_2 \sin (3 x) \\ \end{align*}