10.8.19 problem 25

Internal problem ID [1291]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 25
Date solved : Monday, January 27, 2025 at 04:50:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=\alpha \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 32

dsolve([diff(y(x),x$2)+ 2*diff(y(x),x)+6*y(x) = 0,y(0) = 2, D(y)(0) = alpha],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-x} \left (\sqrt {5}\, \left (\alpha +2\right ) \sin \left (\sqrt {5}\, x \right )+10 \cos \left (\sqrt {5}\, x \right )\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 42

DSolve[{D[y[x],{x,2}]+2*D[y[x],x]+6*y[x]==0,{y[0]==2,Derivative[1][y][0] ==\[Alpha]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{-x} \left (\sqrt {5} (\alpha +2) \sin \left (\sqrt {5} x\right )+10 \cos \left (\sqrt {5} x\right )\right ) \]