50.14.6 problem 1(f)

Internal problem ID [8044]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:37:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

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

\[ y(x)\to \frac {e^x}{2}+c_1 \cos (x)+c_2 \sin (x) \]