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AP EAMCET202315 May 2023Evening ShiftMathematicsDifferential EquationsActual

If and are respectively the order and degree of the differential equation y=e^ ( d y d x + d^2 y d x^2 ) , then the value of + ^ + ^ 2 + + ^ 2023 =

Options

  1. A2²⁰²⁵+2
  2. B2²⁰²⁴+1
  3. C2²⁰²⁴
  4. D2²⁰²⁴-1

Correct answer

C. 2²⁰²⁴

Step-by-step solution

Given differential equation aligned & y=e^ ( d y d x + d^2 y d x^2 ) (y)= d y d x + d^2 y d x^2 & degree =1, order =2 & =2, =1 & Now, + ^ + ^ 2 + .+ ^ 2023 & =2+2^1+2^2+2^3+ +2²⁰²³ & =2+ 2 (2²⁰²³-1 ) 2-1 =2²⁰²⁴ . aligned

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