54.1.2 problem 2

Internal problem ID [8530]
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
Date solved : Monday, January 27, 2025 at 04:09:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {{\mathrm e}^{x}}{4} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{4}+e^{3 x} (c_2 x+c_1) \]