Internal problem ID [5538]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 2(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = -1, y^{\prime }\relax (0) = 2+3 \sqrt {2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve([diff(y(x),x$2)+4*diff(y(x),x)+2*y(x)=0,y(0) = -1, D(y)(0) = 2+3*2^(1/2)],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\left (-2+\sqrt {2}\right ) x}-2 \,{\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 30
DSolve[{y''[x]+4*y'[x]+2*y[x]==0,{y[0]==-1,y'[0]==2+3*Sqrt[2]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\left (\left (2+\sqrt {2}\right ) x\right )} \left (e^{2 \sqrt {2} x}-2\right ) \\ \end{align*}