64.10.27 problem 27

Internal problem ID [13433]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 05:42:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)-6*diff(y(x),x)+8*y(x)=0,y(0) = 1, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = -{\mathrm e}^{2 x}+2 \,{\mathrm e}^{4 x} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]-6*D[y[x],x]+8*y[x]==0,{y[0]==1,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

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