64.2.1 problem 1

Internal problem ID [13261]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:13:24 AM
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 )&=6\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 17

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

\[ y = \left (4 \,{\mathrm e}^{5 x}+2\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

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

\[ y(x)\to e^{-3 x} \left (4 e^{5 x}+2\right ) \]