In Exercises 1–22, solve the differential equation.
y' = xeʸ√(x-2)

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Rewrite the given differential equation as $\frac{dy}{dx} = x e^{y} \sqrt{x - 2}$ to clearly identify the variables and their derivatives.

Separate the variables by dividing both sides by $e^{y}$ and multiplying both sides by $dx$, giving $e^{-y} dy = x \sqrt{x - 2} \, dx$.

Integrate both sides separately: integrate $e^{-y} dy$ with respect to $y$ on the left side, and integrate $x \sqrt{x - 2} \, dx$ with respect to $x$ on the right side.

For the right side integral, consider using a substitution such as $u = x - 2$ to simplify the integral $\int x \sqrt{x - 2} \, dx$.

After integrating both sides, include the constant of integration $C$ and solve for $y$ if possible to express the general solution.

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