# What is a solution to the differential equation #dy/dy=sqrt(1-y)#?

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To solve the differential equation ( \frac{dy}{dx} = \sqrt{1-y} ), follow these steps:

- Separate variables: Write the equation as ( \frac{1}{\sqrt{1-y}} , dy = dx ).
- Integrate both sides: ( \int \frac{1}{\sqrt{1-y}} , dy = \int dx ).
- Solve the integral: ( 2\sqrt{1-y} = x + C ), where ( C ) is the constant of integration.
- Solve for ( y ): ( 1 - y = \left(\frac{x + C}{2}\right)^2 ).
- Determine the constant: Use initial conditions if provided to find the specific value of ( C ).
- Write down the solution: ( y = 1 - \left(\frac{x + C}{2}\right)^2 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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