40.8.5 problem 20

Internal problem ID [6705]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:24:29 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: 0.019 (sec). Leaf size: 26

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

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