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99 Percentile Qs Bank for JEE MainMathematicsDifferential Equations

If x x d y d x +y= x^2 and y(e)=0 , then y (e^2 )=

Options

  1. A0
  2. B1
  3. C1 2
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

We have, aligned & x x d y d x +y= x^2 & d y d x + y x x = 2 x x x & d y d x + y x x = 2 x & IF =e^ 1 x x d x =e^ ( x) & IF = x & aligned Solution of different equation is array rlrl & & y x & = 2 x x d x+c y x & =( x)^2+c put x & =e, y=0 we get 0 & =1+c c=-1 & y x & =( x)^2-1 put & & =e^2 y e^2 & = ( e^2 )^2-1 & & 2 y & =4-1 & & y & = 3 2 & & y (e^2 ) & = 3 2 array

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