20.6.16 problem Problem 38

Internal problem ID [3711]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 38
Date solved : Monday, January 27, 2025 at 07:55:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+diff(y(x),x)-6*y(x)=18*exp(5*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (3 \,{\mathrm e}^{8 x}+4 \,{\mathrm e}^{5 x} c_{1} +4 c_{2} \right ) {\mathrm e}^{-3 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]+D[y[x],x]-6*y[x]==18*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 e^{5 x}}{4}+c_1 e^{-3 x}+c_2 e^{2 x} \]