Internal problem ID [6109]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 8. Nonhomogeneous Equations: Undetermined Coefficients. Exercises Page
142
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+{\mathrm e}^{3 x} c_{1} x +\frac {{\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 26
DSolve[y''[x]-6*y'[x]+9*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x}{4}+e^{3 x} (c_2 x+c_1) \\ \end{align*}