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MHT CET202121 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

I: y^ = y+x x ; II : y^ = x^2+y x^3 ; III : y^ = 2 x y y^2-x^2 S1: Differential equations given by I and II are homogeneous differential equations. S2: Differential equations given by II and III are homogeneous differential equations. S3: Differential equations given by I and III are homogeneous differential equations.

Options

  1. Aonly S 1 is valid
  2. Bboth S1 and S2 are valid
  3. Conly S3 is valid
  4. Donly S2 is valid

Correct answer

C. only S3 is valid

Step-by-step solution

We will check all 3 equations. I : d y d x = y+x x All terms have same degree equal to 1 . II : d y d x = x^2+y y^3 Here all terms have different degrees., III : d y d x = 2 x y y^2-x^2 All terms have same degree equal to 2 .

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