Question

dy/dx = -/1_y^2/1-x^2 solve differential equation​

Answer 1

Answer:

y √(1 - x² ) - x √( 1 - y² ) = k

Step-by-step explanation:

Given--->

dy / dx = √{ (1 - y² ) / ( 1 - x² ) }

Solution---> ATQ,

dy / dx = √(1 - y²) / √(1 - x²)

We solve this differential equation by the method of seperation of variables, in this method we collect terms containing x only in one side and that of y in other side and then integrate the whole equation.

=> dy / √1 - y² = dx / √1 - x²

Now , integrating both sides , we get,

=> ∫ dy / √(1 - y² ) = ∫ dx / √(1 - x² ) + C

We have a formula ,

∫ dp / √(1 - p² ) = Sin⁻¹ p + C , applying it here , we get,

=> Sin⁻¹ y = Sin⁻¹ x + Sin⁻¹ k

=> Sin⁻¹ y - Sin⁻¹ x = Sin⁻¹ k

=> Sin⁻¹ { y √(1 - x² ) - x √(1 - x² ) } = Sin⁻¹ k

=> y √(1 - x² ) - x √(1 - x² ) = k