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Example 39 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 22, 2023 by Teachoo
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Transcript
Example 39 If π¦ = A sinβ‘π₯+B cosβ‘π₯, then prove that π2π¦/ππ₯2 + y = 0. π¦ = A sinβ‘π₯+B cosβ‘π₯ Differentiating π€.π.π‘.π₯ ππ¦/ππ₯ = π(A sinβ‘π₯ + B cosβ‘π₯" " )/ππ₯ ππ¦/ππ₯ = π(A sinβ‘π₯ )/ππ₯ + π(B cosβ‘π₯ )/ππ₯ ππ¦/ππ₯ = A . π(sinβ‘π₯ )/ππ₯ + B . π(cosβ‘π₯" " )/ππ₯ ππ¦/ππ₯ = A cosβ‘π₯" " + B (β sinβ‘π₯) π π/π π = A πππβ‘π" " β B πππβ‘π Again Differentiating π€.π.π‘.π₯ (π^2 π¦)/γππ₯γ^2 = (π (γA cosγβ‘π₯" " " β" γB sinγβ‘π₯))/ππ₯ (π^2 π¦)/γππ₯γ^2 = π(A cosβ‘π₯ )/ππ₯ β π(B sinβ‘π₯" " )/ππ₯ (π^2 π¦)/γππ₯γ^2 = βA sinβ‘π₯ β B cosβ‘π₯ (π^2 π¦)/γππ₯γ^2 = β (A sinβ‘π₯ + B cosβ‘π₯) (π^2 π¦)/γππ₯γ^2 = βy π ππ/π ππ + π = π Hence proved (As π¦ = π΄ π ππβ‘π₯+π΅ πππ β‘π₯)
