5.10 problem 12

Internal problem ID [4292]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number: 12.
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: 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*}