Assertion :The order of the differential equation whose solution is $y = c_{1} e^{2 x + c_{2}} + c_{3} e^{2 x + c_{4}}$ is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.

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 but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
Given $y = c_{1} e^{2 x + c_{2}} + c_{3} e^{2 x + c_{4}}$
$y = (c_{1} e^{c_{2}} + c_{3} e^{c_{4}}) e^{2 x}$
$y = λ e^{2 x}$ (where $λ = c_{1} e^{c_{2}} + c_{3} e^{c_{4}}$ )
$\Rightarrow$ $\frac{d y}{d x} = 2 λ e^{2 x}$ $\Rightarrow$ $\frac{d y}{d x} = 2 y$
$\Rightarrow$ Order of differential equation is 1,
So Assertion (A) is false but Reason (R) is true.

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Similar questions

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 (A) Order and molecularity are same.

Reason (R) Order is determined experimentally and molecularity is the sum of the stoichimetric coeffcient of rate determining elementary step.

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Choose the correct option.

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Assertion :The order of the differential equation whose solution is y=c1e2x+c2+c3e2x+c4 is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.

The correct option is D Assertion is incorrect but Reason is correctGiven y=c1e2x+c2+c3e2x+c4y=(c1ec2+c3ec4)e2xy=λe2x (where λ=c1ec2+c3ec4)⇒ dydx=2λe2x ⇒ dydx=2y⇒ Order of differential equation is 1, So Assertion (A) is false but Reason (R) is true.

Assertion :The order of the differential equation whose solution is $y = c_{1} e^{2 x + c_{2}} + c_{3} e^{2 x + c_{4}}$ is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.