Question

give a clear amswer with all areps. i have trouble understanding limits so explain clearly for positive rating

In each of Problems 17 and 18, determine the values of a, if any, for which all solutions tend to zero as t -> oo; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t oo y" (2a - 1) y a(a - 1) y = 0 17.

Answer 1

Any doubt in amy step then comment belloow.. i will explain..

Forst we write the auxillary equation...and then fjnd the roots

Now we know that solution goes to 0 as t tends to infinity ...if roots of auxillary equation is negative ... Or negative real parts ...

17 4-(2of +1) (2 t1) 42(0-1) 2 2

So we get two roots ...we check where these roots are negative..

Qot1 2 lution thos to mukt be negatice T Jaot (2mt) d e Now l come unbounled Siletian ()(,-)

And in another case , solution unbounded ...when roots have positive value or positive real part...