20.12.10 problem Problem 29

Internal problem ID [3804]
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 29
Date solved : Monday, January 27, 2025 at 08:02:34 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

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

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