If the general solution of some differential equation is $y = a_{1} (a_{2} + a_{3}) cos (x + a_{4}) - a_{5} e^{x + a_{6}}$ , then order of the differential equation is

6

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3

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Solution

The correct option is D $3$
$y = a_{1} (a_{2} + a_{3}) cos (x + a_{4}) - a_{5} e^{x + a_{6}}$
$\Rightarrow y = P cos (x + a_{4}) - a_{5} e^{x} e^{a_{6}}$
$\Rightarrow y = P cos (x + a_{4}) - Q e^{x} \dots (1)$
where $P = a_{1} (a_{2} + a_{3})$ and $Q = a_{5} e^{a_{6}}$

As equation $(1)$ has three independent unknown parameters, order of the differential equation is $3$

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If the general solution of some differential equation is y=a1(a2+a3)cos(x+a4)−a5ex+a6, then order of the differential equation is

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