Assertion :The order of the differential equation whose general solution is $y = c_{1} cos 2 x + c_{2} {s i n}^{2} x + c_{3} e^{x + c_{4}}$ is 2, where $c_{1}, c_{2}, c_{3}, c_{4}$ are arbitrary constants. Reason: Order of a differential equation represents number of independent arbitrary constant in the general solution.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect, Reason is correct

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Solution

The correct option is D Assertion is incorrect, Reason is correct
the reason is correct but the assertion is wrong.
in assertion the number of indepent arbitary constants is $3$ .
the assertion can be written as $c_{1} + (c_{2} - 2 c_{1}) {s i n}^{2} x + c_{3} e^{c_{4}} e^{x} = c_{1} + c {s i n}^{2} x + c_{5} e^{x}$ .

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Similar questions

The order of the differential equation whose general solution is given by $y = (c_{1} + c_{2}) cos (x + c_{3}) - c_{4} e^{x + c_{5}}$ , where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants, is

Assertion (A) Order of the reaction can be zero or fractional.

Reason (R) We cannot determine order from balanced chemical equation.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.
Reason: Equation of the x-axis is y = 0

Choose the correct option.

In the following questions, a statement of assertion is followed by a statement of reason. Mark the correct choice as:
Assertion: The efficiency of $C_{4}$ plant is more than those of $C_{3}$ plant.
Reason : $C_{4}$ plants are more efficient in picking $C O_{2}$

Q. Assertion: In the equation,

y = A sin (k x - ω t)

, particle starts from its mean position

x = 0

and moves towards negative

y -

axis.
Reason: The wave corresponding to given equation is travelling towards positive

x -

direction.

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Assertion :The order of the differential equation whose general solution is y=c1cos2x+c2sin2x+c3ex+c4 is 2, where c1,c2,c3,c4 are arbitrary constants. Reason: Order of a differential equation represents number of independent arbitrary constant in the general solution.

The correct option is D Assertion is incorrect, Reason is correctthe reason is correct but the assertion is wrong.in assertion the number of indepent arbitary constants is 3.the assertion can be written as c1+(c2−2c1)sin2x+c3ec4ex=c1+csin2x+c5ex.