Find the particular solution of the differential equation that satisfies the initial condition.

Question

Find the particular solution of the differential equation that satisfies the initial condition.

dy/dx = 1/(sqrt(4-x^2) , y(0) = π

Answer 1

dy/dx = 1 / √(4 - x²)

Separate variables: dy = 1 / √(4 - x²) dx

Integrate: ∫dy = ∫ [1 / √(4 - x²)]dx

So, y = Sin^-1(x/2) + C

Since y = π when x = 0, π = Sin^-1(0) + C

C = π

y = Sin^-1x + π