49.4.8 problem 2(a)

Internal problem ID [7619]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 03:07:45 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

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