10.9.5 problem 5

Internal problem ID [1307]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:50:35 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+10*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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