10.7.13 problem 13

Internal problem ID [1261]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:48:13 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 41

dsolve([diff(y(x),x$2) +5*diff(y(x),x)+3*y(x) = 0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left (13+5 \sqrt {13}\right ) {\mathrm e}^{\frac {\left (-5+\sqrt {13}\right ) x}{2}}}{26}+\frac {\left (13-5 \sqrt {13}\right ) {\mathrm e}^{-\frac {\left (5+\sqrt {13}\right ) x}{2}}}{26} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 51

DSolve[{D[y[x],{x,2}]+5*D[y[x],x]+3*y[x]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{26} e^{-\frac {1}{2} \left (5+\sqrt {13}\right ) x} \left (\left (13+5 \sqrt {13}\right ) e^{\sqrt {13} x}+13-5 \sqrt {13}\right ) \]