Question

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

Answer 1

Answer:

$y(x) = e^{3x} [Acos x+Bsin x]$

Step-by-step explanation:

Given is a differential equation

$y" - 6y' +10y=0.$

We have characteristic equation as

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

The above quadratic cannot be factorised hence use formula

$m=\frac{6+/-\sqrt{36-40} }{2} \\=3+i, 3-i$

Hence general solution would be

$y(x) = e^{3x} [Acos x+Bsin x]$