35.5.9 problem 9

Internal problem ID [6143]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 9
Date solved : Monday, January 27, 2025 at 01:38:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

\[ y = {\mathrm e}^{2 x} \left (c_1 \sin \left (3 x \right )+c_2 \cos \left (3 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

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

\[ y(x)\to e^{2 x} (c_2 \cos (3 x)+c_1 \sin (3 x)) \]