35.6.6 problem 6

Internal problem ID [6156]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 6
Date solved : Monday, January 27, 2025 at 01:38:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-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)=12*exp(-x),y(x), singsol=all)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{-3 x}+3 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==12*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (3 e^{2 x}+c_2 x+c_1\right ) \]