Let' s use NDSolve to find the solution to a differential equation we already know. u'' = (a^2)u. Now to find a numerical solution, we need acutal numbers for things like a. Also, we need to know the range over which we want to know the solution and the boundary (or initial) conditions (one for each order of the equation). We'll call ours u0 anad up0 for the value of y and its derivative at zero.

a=5/10

u0=2; up0=-a*u0

xmin=0; xmax=10

sol=NDSolve[{u''[x]-a^2*u[x]==0, u[0]==u0, u'[0]==up0}, u, {x, xmin, xmax}]

Now, that doesn' t look too helpful, so let's plot it. We'll also plot the known answer for comparison.

Plot[Evaluate[u[x]/.sol],{x,xmin,xmax}, PlotStyle->Thick,PlotRange->All]

Plot[u0*Exp[-a*x], {x, xmin,xmax},PlotStyle->Thick, PlotRange->All]