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Calculus

Differential Equations, Variable Separable

jee_main_2026_april_4_shift_1

Grade 12

Question:

The solution of the differential equation dy/dx = (1 + y^2)/(1 + x^2) is:

A. tan^{-1} y = tan^{-1} x + C

B. tan^{-1} y = cot^{-1} x + C

C. cot^{-1} y = tan^{-1} x + C

D. sin^{-1} y = sin^{-1} x + C

Step-by-Step Solution

Key Concept: Separate the variables.

Step 1: dy/(1+y^2) = dx/(1+x^2). Step 2: tan^{-1} y = tan^{-1} x + C.

Correct Answer: A

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