Question

If y = e^{m sin₁ x} , prove that (1 - x²) y₂ - x y₁ = m² y.

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Solution

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Differentiating both sides w.r.t. x, we get,

(1 - x²). 2 y₁ y₂ + y₁^{2 (-2 x) = 2 m² y y_i}

Dividing both sides by 2 y₁ , we get,

(1 - x²) y₂ - x y₁ = m² y

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Continuity And Differentiability

If y = e^{m sin₁ x} , prove that (1 - x²) y₂ - x y₁ = m² y.

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If y = e^{m sin₁ x} , prove that (1 - x²) y₂ - x y₁ = m² y.