10.7.24 problem 26

Internal problem ID [1272]
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 : 26
Date solved : Monday, January 27, 2025 at 04:49:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 23

dsolve([diff(y(x),x$2) +5*diff(y(x),x)+6*y(x) = 0,y(0) = 2, D(y)(0) = beta],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (6+\beta \right )+{\mathrm e}^{-3 x} \left (-\beta -4\right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[{D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==0,{y[0]==2,Derivative[1][y][0] ==\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (-\beta +(\beta +6) e^x-4\right ) \]