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AP EAMCET · Maths · Differential Equations

Statement (I) The elimination of arbitrary constants from \(\alpha, \beta\) and \(\gamma\) from \(y=(\alpha+\beta+\gamma) x\) results in a differential equation of order three.
Statement (II) The elimination of arbitrary constants \(\alpha, \beta\) and \(\gamma\) from \(y=\alpha x+\beta \sin x+\gamma e^x\) results in a differential equation of order three.

  1. A I is true and II is false
  2. B I is false and II is false
  3. C I is true and II is true
  4. D I is false and II is true
Verified Solution

Answer & Solution

Correct Answer

(D) I is false and II is true

Step-by-step Solution

Detailed explanation

Statement I \(\Rightarrow \quad y=(\alpha+\beta+\gamma) x\) Differentiate both sides w.r.t. \(x\), we get \(\frac{d y}{d x}=(\alpha+\beta+\gamma)=k\) Here, order \(=1\) So, statement \(\mathrm{I}\) is false. Statements II : \(y=\alpha x+\beta \sin x+\gamma e^x\) Differentiate…