Internal problem ID [177]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 37.
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: 0.0 (sec). Leaf size: 15
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: 0.003 (sec). Leaf size: 22
DSolve[2*y''[x]-y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x/2}+c_2 e^x \\ \end{align*}