Internal problem ID [5098]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page
147
Problem number: Example 3.19.
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: 0.015 (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: 0.004 (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*}