73.8.15 problem 13.2 (i)

Internal problem ID [15223]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (i)
Date solved : Tuesday, January 28, 2025 at 07:50:20 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*diff(y(x),x)=9*exp(-3*x),y(x), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-4 x}}{4}-3 \,{\mathrm e}^{-3 x}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+4*D[y[x],x]==9*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 e^{-3 x}-\frac {1}{4} c_1 e^{-4 x}+c_2 \]