Internal problem ID [202]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 8.
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*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{3 x} \sin \left (2 x \right )+c_{2} {\mathrm e}^{3 x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 26
DSolve[y''[x]-6*y'[x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}