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`        y’’+ay’+by=0 be differential equation where a & b are constants, show that the general solution tends to zero as x tends to infinity iff both a & b are positive`
4 years ago

```							This is a higher level education which is taght in coleges/universities.Let y = e^mx be the soln. of the given eqn.thenwe get quadratic,m^2 + am + b = 0m1 = (-a + root(a^2 – 4b))/2m2 =  (-a - root(a^2 – 4b))/2As roots are distinct,The general soln. is: Yg = c1e^(m1x) + c2 e^(m2x)where c1 and c2 are the constants. orYg =  c1e^x*(-a + root(a^2 – 4b))/2   + c2e^x*(-a - root(a^2 – 4b))/2as x tends to infinityYg tends to zero hence.for a>0andb>0
```
3 years ago
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