Internal problem ID [5628]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \relax (x ) = \frac {\left (-9 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) {\mathrm e}^{-x}}{8}+\frac {{\mathrm e}^{x}}{8} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 32
DSolve[{y''[x]+2*y'[x]+5*y[x]==Exp[x],{y[0]==-1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} e^{-x} \left (e^{2 x}-\sin (2 x)-9 \cos (2 x)\right ) \\ \end{align*}