10.9.10 problem 10

Internal problem ID [1312]
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 : 10
Date solved : Monday, January 27, 2025 at 04:50:43 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 32

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

\[ y(x)\to e^{-x/2} \left (c_2 \cos \left (\frac {x}{2}\right )+c_1 \sin \left (\frac {x}{2}\right )\right ) \]