Let y(x) and y (x) forms a fundamental set of solutions to the differential equation dy...

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Let y(x) and y₂ (x) forms a fundamental set of solutions to the differential equation d²y dy dx² + P(x)+Q(x) y = 0, 0≤x≤ b dx where P(x) and Q(x) are continuous in [a, b] and xo is a point in (a, b). Then, Both y(x) and y₂ (x) cannot have a local maximum at xo. Both y(x) and y₂ (x) cannot have a local minimum at xo ₁(x) cannot have a local maximum and y₂ (x) cannot have a local minimum at x simultaneouly. Both y(x) and y₂ (x) cannot vanish at x simultaneouly. Let y(x) and y₂ (x) forms a fundamental set of solutions to the differential equation d²y dy dx² + P(x)+Q(x) y = 0, 0≤x≤ b dx where P(x) and Q(x) are continuous in [a, b] and xo is a point in (a, b). Then, Both y(x) and y₂ (x) cannot have a local maximum at xo. Both y(x) and y₂ (x) cannot have a local minimum at xo ₁(x) cannot have a local maximum and y₂ (x) cannot have a local minimum at x simultaneouly. Both y(x) and y₂ (x) cannot vanish at x simultaneouly.