20.7.1 problem Problem 25

Internal problem ID [3716]
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 25
Date solved : Monday, January 27, 2025 at 07:55:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

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

\[ y(x)\to 3 e^x+c_1 \cos (x)+c_2 \sin (x) \]