20.6.20 problem Problem 42

Internal problem ID [3715]
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 42
Date solved : Monday, January 27, 2025 at 07:55:49 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+6*diff(y(x),x)=6*exp(-x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} c_{2}}{3}-\frac {{\mathrm e}^{-2 x} c_{1}}{2}-3 \,{\mathrm e}^{-x}+c_3 \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]==6*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 e^{-x}-\frac {1}{3} c_1 e^{-3 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]