Determine if the differential equation $y^{'} = x e^{y}$ is separable, and if so, write it in the form $h (y) d y = g (x) d x$ .
NOTE: If the equation is not separable, indicate with the checkbox.
$d y =$ $d x$ Not separable.

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Final Answer: The differential equation $y^{'} = x e^{y}$ is separable and can be written in the form $e^{- y} d y = x d x$ .

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Step 1 ：The given differential equation is $y^{'} = x e^{y}$ . A differential equation is said to be separable if it can be written in the form $h (y) d y = g (x) d x$ .

Step 2 ：In this case, we can see that the function $y^{'}$ is a product of a function of $x$ and a function of $y$ . Therefore, it seems that the equation is separable.

Step 3 ：We can write it in the form $h (y) d y = g (x) d x$ by dividing both sides by $e^{y}$ and multiplying both sides by $d x$ . This gives us $h (y) = e^{- y}$ and $g (x) = x$ .

Step 4 ：Final Answer: The differential equation $y^{'} = x e^{y}$ is separable and can be written in the form $e^{- y} d y = x d x$ .

Determine if the differential equation y′=xey is separable, and if so, write it in the form h(y)dy=g(x)dx.NOTE: If the equation is not separable, indicate with the checkbox.dy= dx Not separable.

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Determine if the differential equation $y^{'} = x e^{y}$ is separable, and if so, write it in the form $h (y) d y = g (x) d x$ .
NOTE: If the equation is not separable, indicate with the checkbox.
$d y =$ $d x$ Not separable.