10.7.9 problem 9

Internal problem ID [1257]
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 : 9
Date solved : Monday, January 27, 2025 at 04:48:04 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 )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 21

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

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