7.8.24 problem 37

Internal problem ID [238]
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 : 37
Date solved : Monday, January 27, 2025 at 02:42:52 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(2*diff(y(x),x$2)-diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{2}}+c_2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to c_1 e^{-x/2}+c_2 e^x \]