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If y(x) satisfies the differential equation y^ -y x=2 x x and y(0)=0 , then

Options

  1. Ay ( 4 )= ² 8 2
  2. By^ ( 4 )= ² 18
  3. Cy ( 3 )= ² 9
  4. Dy^ ( 3 )= 4 3 + 2 ² 3 3

Correct answer

A. y ( 4 )= ² 8 2

Step-by-step solution

d y d x -y x=2 x x I.F. =e^ - x d x = x y x= 2 x d x=x²+c Now, y(0)=0 c=0, y=x² x y^ =2 x x+x² x x Now, y ( 4 )= ² 16 2 = ² 8 2 y ( 3 )= ² 9 2= 2 ² 9 y^ ( 4 )= 2 4 2 + ² 8 2 1= ² 8 2 + 2 y^ ( 3 )= 2 3 2+ 2 ² 9 3 = 2 ² 3 3 + 4 3

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