Question

dy/dx=√(y-x) plz solve it

Answer 1

$\textbf{Answer :}$

Given that,

dy/dx = √(y - x) ...(i)

Let, y - x = z²

∴ dy/dx - 1 = 2z dz/dx

⇒ dy/dx = 1 + 2z dz/dx

From (i), we get

1 + 2z dz/dx = z

⇒ 2z dz/dx = z - 1

⇒ 2z/(z - 1) dz = dx

⇒ 2 (z - 1 + 1)/(z - 1) dz = dx

⇒ 2 dz + 2 dz/(z - 1) = dx

∴ integrating, we get

2 ∫ dz + 2 ∫ dz/(z - 1) = ∫ dx + c, where c is integral constant

⇒ 2z + 2 log(z - 1) = x + c

⇒ 2 √(y - x) + 2 log{√(y - x) - 1} = x + c,

which is the required solution.

#$\textbf{MarkAsBrainliest}$

Answer 2

please see attached file