Internal problem ID [5530]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 1(o).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(2*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[2*y''[x]+y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (c_1 e^{3 x/2}+c_2\right ) \\ \end{align*}