50.14.11 problem 2(c)

Internal problem ID [8049]
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 : 2(c)
Date solved : Monday, January 27, 2025 at 03:38:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&={\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 28

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=exp(x),y(0) = -1, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}}{8}+\frac {\left (-\sin \left (2 x \right )-9 \cos \left (2 x \right )\right ) {\mathrm e}^{-x}}{8} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 32

DSolve[{D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==Exp[x],{y[0]==-1,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{-x} \left (e^{2 x}-\sin (2 x)-9 \cos (2 x)\right ) \]