rafaelac5803 rafaelac5803
  • 13-09-2019
  • Mathematics
contestada

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

Respuesta :

AlonsoDehner AlonsoDehner
  • 17-09-2019

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]

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