73.11.34 problem 17.6 (d)

Internal problem ID [15348]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.6 (d)
Date solved : Tuesday, January 28, 2025 at 07:53:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 23

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{2 x} \left (2 \sin \left (3 x \right )-3 \cos \left (3 x \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+13*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{2 x} (3 \cos (3 x)-2 \sin (3 x)) \]