Answer:
[tex]y(x) = e^{3x} [Acos x+Bsin x][/tex]
Step-by-step explanation:
Given is a differential equation
[tex]y" - 6y' +10y=0.[/tex]
We have characteristic equation as
[tex]m^2-6m+10 =0[/tex]
The above quadratic cannot be factorised hence use formula
[tex]m=\frac{6+/-\sqrt{36-40} }{2} \\=3+i, 3-i[/tex]
Hence general solution would be
[tex]y(x) = e^{3x} [Acos x+Bsin x][/tex]
