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Class 12 Maths Chapter 9: Differential Equations Assertion-reason questions with answers

2 assertion-reason questions on Differential Equations, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The differential equation (y‴)2 + log (y′) = x has order 3, and its degree is not defined. Reason (R): The degree of a differential equation is defined only when it is a polynomial equation in its derivatives.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

The highest derivative is y‴, so the order is 3. log (y′) is not a polynomial in y′, so by R the degree is not defined. R is exactly the reason for the second half of A.

Question 2
Assertion (A): The differential equation dydx = y − xy + x is homogeneous. Reason (R): The function x2 − 3xy + y2 is a homogeneous function of degree 2.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A: F(λx, λy) = λ(y − x)/(λ(y + x)) = λ0 F(x, y), so F has degree zero and the equation is homogeneous. R: each term has degree 2, so R is true. But A rests on F being of degree zero, a fact about a different function; R does not explain A.

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