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KCET2022MathematicsDifferential Equations

If d y d x + y x =x^2 , then 2 y(2)-y(1)=

Options

  1. A11 4
  2. B15 4
  3. C9 4
  4. D13 4

Correct answer

B. 15 4

Step-by-step solution

d y d x + y x =x^2 On comparing to d y d x +P(x) y=Q(x) aligned & P(x)= 1 x , Q(x)=x^2 & IF =e^ P d x =e^ 1 x d x =e^ x =x & y ( IF )= Q(x)( IF ) d x+C & y x= x^2 x d x+C= x^4 4 +C & y= x^3 4 + C x & y(2)= 2^3 4 + C 2 =2+ C 2 & y(1)= 1 4 + C 1 = 1 4 +C & 2 y(2)-y(1)=2 (2+ C 2 )- ( 1 4 +C ) &=4+C- 1 4 -C= 15 4 aligned

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