Statement (I) : The elimination of arbitrary constants from $α, β$ and $γ$ from $y = (α + β + γ) x$ results in a differential
equation of order three
Statement (II) : The elimination of arbitrary constant $α, β$ and $γ$ from $y = (αx + β \sin x + {γe}^{x}) x$ results in a differential equation of order three Make the correct choice of the following

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I is true and II is true

I is false and II is true

I is true and II is false

I is false and II is false

answer is D.

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Detailed Solution

$\begin{array}{l} S t a t e m e n t (I) : G i v e n E q u a t i o n y = (α + β + γ) \\ O r d e r = 1 [∵ α + β + γ i s o n e o r b i t a r y c o n s \tan t] \\ F a l s e \\ S t a t e m e n t (I I) : G i v e n E q u a t i o n y = α x + β \sin x + γ e^{x} \\ O r d e r = 3 \\ T r u e \end{array}$