What is the general solution of the differential equation y''+4y=0?

kadirsmr9d 2022-09-12 Answered
What is the general solution of the differential equation y + 4 y = 0 ?
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Answers (1)

wegpluktee3
Answered 2022-09-13 Author has 12 answers
We have:
y + 4 y = 0
This is a second order linear Homogeneous Differentiation Equation. The standard approach is to look at the Auxiliary Equation, which is the quadratic equation with the coefficients of the derivatives, i.e.
m 2 + 4 = 0
This has two distinct complex solutions:
m = ± 2 i , or m = 0 ± 2 i
And so the solution to the DE is;
          y = e 0 ( A cos 2 x + B sin 2 x ) Where A,B are arbitrary constants
y = A cos 2 x + B sin 2 x

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