The order of differential equation of family of curves given by $y = a_{1} (a_{2} + a_{3}) \cdot cos (x + a_{4}) - a_{5} e^{x + a_{6}},$ is

6

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5

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4

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3

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Solution

The correct option is D $3$
Substitute $λ_{1} = a_{1} (a_{2} + a_{3})$
$λ_{2} = - a^{5} \cdot e^{a_{6}}$
$y = λ_{1} cos (x + a_{4}) - a^{5} \cdot e^{x} \cdot e^{a_{6}} = λ_{1} cos (x + a_{4}) - λ_{2} e^{x}$

we made it to least number of arbitrary constants.
So the order is the total number of arbitrary constants
Therefore order is $3$

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The order of differential equation of family of curves given by $y = a_{1} (a_{2} + a_{3}) \cdot cos (x + a_{4}) - a_{5} e^{x + a_{6}},$ is