Question

Determine whether each first-order differential equation is separable, linear, both, or neither.

1. dy/dx+eˣ*y²=x ²*y ²

Answer 1

The given first-order differential equation is neither separable nor linear.

Step-by-step explanation:

The given first-order differential equation is:

dy/dx + eˣ*y² = x²*y²

To determine whether this differential equation is separable, linear, both, or neither, we need to analyze its structure. For a differential equation to be separable, it should be possible to separate the variables on one side of the equation. For a differential equation to be linear, each term involving y and its derivatives must be raised to the power of 1. Examining the given equation, we can see that it is neither separable nor linear because we have y raised to the power of 2. Therefore, the answer is neither.