20.7.4 problem Problem 28

Internal problem ID [3719]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 28
Date solved : Monday, January 27, 2025 at 07:55:58 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 31

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

\[ y(x)\to c_1 e^{-x}+e^{2 x} \left (\frac {5 x}{3}-\frac {5}{9}+c_2\right ) \]