The differential equation representing the family of curves y = a (λ x + α) is: - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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The differential equation representing the family of curves y = a sin (λ x + α) is:

Solution & Step-by-step Explanation

Given y = a sin (λ x + α) .Differentiating once: \frac{d y}{d x} = aλ cos (λ x + α) Differentiating a second time: \frac{d ^{2} y}{d x ^{2}} = - a λ^{2} sin (λ x + α) Substitute y = a sin (λ x + α) into the equation: \frac{d ^{2} y}{d x ^{2}} = - λ^{2} y \frac{d ^{2} y}{d x ^{2}} + λ^{2} y = 0

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The differential equation representing the family of curves y = a sin (λ x + α) is:

\frac{d ^{2} y}{d x ^{2}} + λ^{2} y = 0

\frac{d ^{2} y}{d x ^{2}} - λ^{2} y = 0

\frac{d ^{2} y}{d x ^{2}} + λ y = 0

None of the above

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