Consider the differential equation y” + 9y = 0 with the boundary conditions, y(0) = 0, y(2π) = 1, then the differential equation hasa)A unique solutionb)A singly infinite family of solutionsc)No solutiond)At least two solutionsCorrect answer is option 'C'. Can you explain this answer?

Question

Consider the differential equation y&rdquo; + 9y = 0 with the boundary conditions, y(0) = 0, y(2&pi;) = 1, then the differential equation hasa)A unique solutionb)A singly infinite family of solutionsc)No solutiond)At least two solutionsCorrect answer is option 'C'. Can you explain this answer?

Answer

We have (D² + 9)y = 0

⇒ y(x) = c₁cos 3x + c₂sin3x

y(0) = 0 ⇒c₁ = 0

y(2π) = 1 ⇒ c₁ = 1

⇒ DE has no solution.

Answer

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