73.17.39 problem 39

Internal problem ID [15573]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 08:02:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=10*exp(-3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \left (c_{1} x +5 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==10*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (5 x^2+c_2 x+c_1\right ) \]