What is the integrating factor of the differential equation (1 + y²) dx = (tan⁻¹y − x) dy? A. e^(tan⁻¹y) B. e^(−tan⁻¹y) C. tan⁻¹y D. 1/(1+y²) Answer: A) e^(tan⁻¹y) Explanation: Divide by (1+y²)dy: dx/dy + x/(1+y²) = tan⁻¹y / (1+y²). This is linear in x. P = 1/(1+y²). IF = e^(∫dy/(1+y²)) = e^(tan⁻¹y).

imo class 12 differential equations

What is the integrating factor of the differential equation (1 + y²) dx = (tan⁻¹y − x) dy?

VAVidaara Admin Asked 6d ago 0 views 0 answers

What is the integrating factor of the differential equation (1 + y²) dx = (tan⁻¹y − x) dy?

Answer: A) e^(tan⁻¹y)

Explanation: Divide by (1+y²)dy: dx/dy + x/(1+y²) = tan⁻¹y / (1+y²). This is linear in x. P = 1/(1+y²). IF = e^(∫dy/(1+y²)) = e^(tan⁻¹y).