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KCET2020MathematicsVector Algebra

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c₁ y= (c₂+c₃ ) e^ x+c₄ is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

We have, c₁ y= (c₂+c₃ ) e^ x+c₄ aligned & y= ( c₂+c₃ c₁ ) e^ c₄ e^ x & y=c e^ x where c= c₂+c₃ c₁ e^ c₄ aligned Taking log on both sides, we get aligned & y= (c e^ x ) & y= c+x e & y= c+x & On differentiating w.r.t.x, we get & 1 y d y d x =1 d y d x =y & order =1 aligned

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