71.13.2 problem 2

Internal problem ID [14522]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:42:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method

✓ Solution by Maple

Time used: 9.644 (sec). Leaf size: 29

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

\[ y = \frac {{\mathrm e}^{x} \left (2 y \left (0\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (y^{\prime }\left (0\right )-y \left (0\right )\right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 24

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

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