48.2.3 problem Example 3.19

Internal problem ID [7519]
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
Date solved : Monday, January 27, 2025 at 03:04:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_{1} \sin \left (2 x \right )+c_{2} \cos \left (2 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 \cos (2 x)+c_1 \sin (2 x)) \]