64.10.25 problem 25

Internal problem ID [13431]
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 : 25
Date solved : Tuesday, January 28, 2025 at 05:42:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(0) = 3, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{7 x}+1\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-D[y[x],x]-12*y[x]==0,{y[0]==3,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

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