20.12.8 problem Problem 27

Internal problem ID [3802]
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 8.10, Chapter review. page 575
Problem number : Problem 27
Date solved : Monday, January 27, 2025 at 08:02:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-4*y(x)=5*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-4*y[x]==5*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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