Class 12 Differential Equations · Assertion Reason1 Markslinear_differential_equations

Class 12 Maths · Differential Equations · Assertion Reason #23

Assertion (A): A solution of (1 + x²)y′ + y = arctan x is ye^(arctan x) = (arctan x − 1)e^(arctan x) + C. Reason (R): An equation y′ + Py = Q, with P and Q functions of x or constants, is linear.

(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.

With t = arctan x, IF = eᵗ and ∫teᵗdt = (t − 1)eᵗ. R states linearity but not the integration that establishes A.

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Class 12 Maths · Differential Equations · Assertion Reason #23

✅ Step-by-Step Solution

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