50.14.19 problem 3(c)

Internal problem ID [8057]
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 : 3(c)
Date solved : Monday, January 27, 2025 at 03:40:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{1} -\frac {3 \cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {\sin (x)}{10}-\frac {3 \cos (x)}{10}+c_1 e^{-x}+c_2 e^{2 x} \]