7.8.5 problem 5

Internal problem ID [219]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:42:38 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 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: 0.010 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 15

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

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