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.
- A I is true and II is false
- B I is false and II is false
- C I is true and II is true
- D I is false and II is true
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…
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