8.9.8 problem 8

Internal problem ID [852]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 8
Date solved : Wednesday, February 05, 2025 at 04:34:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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