Class 12 Differential Equations · Assertion Reason1 Marksseparable_differential_equations

Class 12 Maths · Differential Equations · Assertion Reason #26

Assertion (A): On x > 0, a solution of e^(y′) = x² is y = 2(x ln x − x) + C. Reason (R): An integrating factor of (1 + x²)y′ + y = arctan x is e^(arctan x).

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true but R is false.
(D) A is false but R is true.

✅ Step-by-Step Solution

Final Answer: Option (B): Both A and R are true, but R does not correctly explain A.

A follows from y′ = 2ln x and integration by parts. R follows from P = 1/(1 + x²), independently of A.

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Class 12 Maths · Differential Equations · Assertion Reason #26

✅ Step-by-Step Solution

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