20.6.18 problem Problem 40

Internal problem ID [3713]
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 40
Date solved : Monday, January 27, 2025 at 07:55:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=4 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{4 x}+3 c_{1} {\mathrm e}^{3 x}+3 c_3 \,{\mathrm e}^{x}+3 c_{2} \right ) {\mathrm e}^{-2 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 37

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

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