saykblahwah1758 saykblahwah1758
  • 13-09-2019
  • Mathematics
contestada

Find a general solution of y" + 4y = 0.

Respuesta :

jorgezarate
jorgezarate jorgezarate
  • 16-09-2019

Answer:

[tex]y(x)=C_{1}cos2x+C_{2}sin(2x)[/tex]

Step-by-step explanation:

It is a linear homogeneous differential equation with constant coefficients:

y" + 4y = 0

Its characteristic equation:

r^2+4=0

r1=2i

r2=-2i

We use these roots in order to find the general solution:

[tex]y(x)=C_{1}cos2x+C_{2}sin(2x)[/tex]

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