10.7.19 problem 21

Internal problem ID [1267]
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 : 21
Date solved : Monday, January 27, 2025 at 04:48:27 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 25

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

\[ y = \frac {\left (2 \alpha -2\right ) {\mathrm e}^{-x}}{3}+\frac {{\mathrm e}^{2 x} \left (\alpha +2\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 29

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

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