10.7.10 problem 10

Internal problem ID [1258]
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 : 10
Date solved : Monday, January 27, 2025 at 04:48:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve([diff(y(x),x$2) +4*diff(y(x),x)+3*y(x) = 0,y(0) = 2, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-3 x}}{2}+\frac {5 \,{\mathrm e}^{-x}}{2} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+3*y[x]==0,{y[0]==2,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-3 x} \left (5 e^{2 x}-1\right ) \]