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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

Let $v=\left[\begin{array}{c}{v}_{1}\left(x\right)\\ {v}_{2}\left(x\right)\end{array}\right]$ where .

(a) the second-order equation above can be written as a system of first-order equations $\frac{d}{dx}v=Av$ ,

where A is the matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$. Find a, b, c and d.

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

for arbritrary constants ${c}_{1},{c}_{2}.$ Find the real integers h,k,m,n which are ordered such that .