Internal problem ID [657]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+10 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+10*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} \sin \left (3 x \right )+c_{2} {\mathrm e}^{x} \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[y''[x]-2*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \cos (3 x)+c_1 \sin (3 x)) \\ \end{align*}