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Manipal MET2014MathematicsDifferential Equations

The real value of m for which the substitution y=u^m will transform the differential equation 2 x^4 y d y d x +y^4=4 x^6 into a homogeneous equation, is

Options

  1. Am=0
  2. Bm=1
  3. Cm= 3 2
  4. Dm= 2 3

Correct answer

C. m= 3 2

Step-by-step solution

aligned & y=u^m d y d x =m u^ m-1 d u d x & Hence, 2 x^4 m u^ m-1 u^m d u d x +u^ 4 m =4 x^6 & d u d x = 4 x^6-u^ 4 m 2 m x^4 u^ 2 m-1 & 4 m=6 m= 3 2 aligned

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