Solve the initial value problem y'=\sqrt{1-y^2}, \quad y(0)=0

Question:

Solve the initial value problem {eq}\displaystyle y'=\sqrt{1-y^2}, \quad y(0)=0 {/eq}

Separation of Variables:

One of the methods of finding solutions of differential equations is separation of variables.

As its name suggests, this technique finds the solution of a differential equation by separating the variables into the two sides of the equation.

If we integrate it, the solution can be obtained.

We split first the variables {eq}x {/eq} and {eq}y {/eq}:

{eq}\begin{align*} \displaystyle y' & =\sqrt{1-y^2}\\ \frac{\mathrm{d}y}{\mathrm{d}x}&...

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