Internal problem ID [4085]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.23, page 220.
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 }+5 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)+5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x} \sin \left (2 x \right )+c_{2} {\mathrm e}^{x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[y''[x]-2*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}