Question

d^2y/dx^2-y=0 solve the homogenious linear differential equation
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Answer 1

Answer:

The general form of the second order linear differential equation is as follows

d2y / dx2 + P(x) dy / dx + Q(x) y = R(x)

If R(x) is not equal to zero, the above equation is said to be inhomogeneous.

If R(x) = 0, the above equation becomes

d2y / dx2 + P(x) dy / dx + Q(x) y = 0

and is called second order linear homogeneous differential equation.

Theorem

If y1(x) and y2(x) are two linearly independent solutions of the homogeneous differential equation d2y / dx2 + P(x) dy / dx + Q(x) y = 0, then the general solution of the above equation may be written as

y(x) = A y1(x) + B y2(x)

where A and B are constants.

NOTE: Functions y1(x) and y2(x) are linearly independent if one is not a multiple of the other.