73.15.2 problem 22.1 (b)

Internal problem ID [15433]
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 : 22.1 (b)
Date solved : Tuesday, January 28, 2025 at 07:55:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=27*exp(6*x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+3 \,{\mathrm e}^{6 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==27*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
 

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