Internal problem ID [168]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+13 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+13*y(x)=0,y(0) = 2, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} \left (3 \sin \left (2 x \right )+2 \cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[{y''[x]+6*y'[x]+13*y[x]==0,{y[0]==2,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} (3 \sin (2 x)+2 \cos (2 x)) \\ \end{align*}