Assertion (A): y = x^2 + C is a solution of dy/dx = 2x for every constant C. Reason (R): The derivative of a constant is 0.

Differential Equations · Question 23 of 67

Question 23

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Assertion (A): $y = x^2 + C$ is a solution of $\frac{dy}{dx} = 2x$ for every constant $C$ .
Reason (R): The derivative of a constant is 0.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$\frac{d}{dx}(x^2 + C) = 2x + 0 = 2x$ , so A is true.
It works for every $C$ precisely because the constant's derivative is 0, so R explains A.

Concept: Constants in the general solution
Typical timeTypical: 60 s
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Assertion (A): y=x2+Cy = x^2 + Cy=x2+C is a solution of dydx=2x\frac{dy}{dx} = 2xdxdy​=2x for every constant CCC.Reason (R): The derivative of a constant is 0.

Explanation

Assertion (A): $y = x^2 + C$ is a solution of $\frac{dy}{dx} = 2x$ for every constant $C$ .
Reason (R): The derivative of a constant is 0.