49.5.1 problem 1(a)

Internal problem ID [7625]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 59
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:07:58 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 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: 0.011 (sec). Leaf size: 17

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

\[ y = -\frac {{\mathrm e}^{-x}}{4}+\frac {{\mathrm e}^{3 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} e^{-x} \left (e^{4 x}-1\right ) \]