Question

Find a general solution of y" - 6y' +10y=0.

Answer 1

`y(x) = e^(3x) [Acos x+Bsin x]`

Explanation:

Given is a differential equation

`y`

We have characteristic equation as

`m^2-6m+10 =0`

The above quadratic cannot be factorised hence use formula

`m=(6+/-√(36-40) )/(2) \\=3+i, 3-i`

Hence general solution would be

`y(x) = e^(3x) [Acos x+Bsin x]`