Question

What is the solution of the differential equation \(\rm \cos \left(\frac{dx}{dy} \right ) - a = 0\) ?

Where a is an arbitrary constant.

1. ​y = x cos-1 a  + c
2. ​x = cos-1 a  + c
3. x = y cos-1 a  + c
4. cos (x + y) + c = 0

Answer 1

Correct Answer - Option 3 : x = y cos-1 a  + c

Calculation:

Given: \(\rm \cos \left(\frac{dx}{dy} \right ) - a = 0\)

⇒ \(\rm \cos \left(\frac{dx}{dy} \right ) = a \)

⇒ \(\rm \frac{dx}{dy}\) = cos^-1 a

⇒ dx = cos-1 a dy

Integrating both sides, we get

⇒ ∫ dx = ∫ cos-1 a dy

⇒ x = cos-1 a × y  + c

⇒ x = y cos-1 a  + c