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Manipal MET2015MathematicsDifferential Equations

Solution of the differential equation 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

Options

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

Correct answer

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

Step-by-step solution

We have, x=e^ x y d y d x array ll & x=x y d y d x & y d y= x x d x & y d y= x d( x) array On integrating both sides, we get y^2 2 = ( _ x )^2 2 +C array ll & y^2= ( _ x )^2+2 C & y= ( _ x )^2+2 C array

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