64.11.30 problem 30

Internal problem ID [13480]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 05:45:03 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*}

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=27*exp(-6*x),y(0) = -2, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \left (3 x -5\right ) {\mathrm e}^{-3 x}+3 \,{\mathrm e}^{-6 x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==27*Exp[-6*x],{y[0]==-2,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-6 x} \left (e^{3 x} (3 x-5)+3\right ) \]