The problem Solve: d^n y/dx^n = f(x, y, y\',..., y^(n - 1) Subject to y(x_0) = y

Question

The problem Solve: d^n y/dx^n = f(x, y, y',..., y^(n - 1) Subject to y(x_0) = y_0, y'(x_0) = y_1,..., y^(n - 1)(x_0) = y_n-1. where y0, y1... yn-1 are arbitrarily specified real constants, is called an______. The values of y(x) and its first n - 1 derivatives at a single point x_0 y'(x0) = y1,..., y^(n-1) (x0) = y_n-1, are called______. initial-value problem; initial conditions boundary value problem; exact conditions exact value problem; boundary conditions intermediate value problem; boundary conditions

Explanation / Answer

Option (a) ; Initial Value problem; initial conditions

is the correct answer.

Reason:

As you may notice, Initial values of the variables are provided.

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