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Manipal MET2010MathematicsDifferential Equations

Solution of the differential equation aligned x=1+x y d y d x + (x y)^2 2! ( & . d y d x )^2 + (x y)^3 3! ( d y d x )^3+ is aligned

Options

  1. Ay= _e(x)+c
  2. By= ( _e x )^2+c
  3. Cy= ( _e x )^2+2 c
  4. Dx y=x^y+k

Correct answer

C. y= ( _e x )^2+2 c

Step-by-step solution

The given differential equation can be written as x=e^ x y d y d x x=x y d y d x y d y= x x d x y d y= x d( x) On integrating, we get y^2 2 = ( x)^2 2 +c y^2= ( _e x )^2+2 c y= ( _e x )^2+2 c

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