3 years ago

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

Mathematics

1 answer:

klio [65]3 years ago

8 0

Answer:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

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:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

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