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BITSAT2015MathematicsDifferential EquationsActual

If ( x ) is a differential function, then the solution of the differential equation dy + y ^ ( x )- ( x ) . . ^ (x) d x=0, is

Options

  1. Ay= (x)-1 +C e^ - (x)
  2. By (x)= (x) ²+C
  3. Cy e^ (x) = (x) e^ (x) +C
  4. Dy- (x)= (x) e^ - (x)

Correct answer

A. y= (x)-1 +C e^ - (x)

Step-by-step solution

Given differential equation is dy + y ^ (x)- (x) ^ (x) d x=0 dy dx + ^ ( x ) y = ( x ) ^ ( x ) which is a linear differential equation with P= ^ (x), Q= (x) ^ (x) and I F=e^ ^ (x) d x =e^ (x) Solution is y e^ (x) = (x) ^ (x) e^ (x) d x+C y e^ (x) = (x) e^ (x) ^ (x) d x+C y e^ (x) = (x) e^ (x) - ^ (x) e^ (x) d x+C y e^ (x) = (x) e^ (x) -e^ (x) +C y= (x)-1]+C e^ - (x)

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