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  3. consider the secondorder ordinary differential equation d2ydx2dydx2y0 let vv1xv2x...

Question: consider the secondorder ordinary differential equation d2ydx2dydx2y0 let vv1xv2x...

Question details

Consider the second-order ordinary differential equation d2ydx2-dydx-2y=0  *

Let v=v1(x)v2(x) where v1(x)=y(x) and v2(x)=dydx.

(a) the second-order equation above can be written as a system of first-order equations ddxv=Av ,

where A is the matrix abcd. Find a, b, c and d.

(b) The general solution of the differential equation * can be written as

y(x)=c1exp((h+ik)x)+c2exp((m+in)x)  for arbritrary constants c1,c2. Find the real integers h,k,m,n which are ordered such that hm and kn.

 

 

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