Question

dy Classify the following DE: e*. dx + 3y = x²y Select one: a. Seperable and Bernoulli b. Linear and not seperable C. Seperable and not linear d. Both seperable and linear.

Answer 1

The given differential equation, e*. dx + 3y = x²y, is both separable and linear.

Step-by-step explanation:

To classify the given differential equation, e*. dx + 3y = x²y, we need to analyze its form and properties.

First, let's check if the equation is separable. A separable differential equation can be written in the form dy/dx = f(x)g(y), where f(x) and g(y) are functions of x and y, respectively. In the given equation, we can rewrite it as e*. dx = (x²y - 3y)dx. By separating the variables, we have dy/(x²y - 3y) = e*. dx.

Next, let's check if the equation is linear. A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In the given equation, we have 3y on the left side and x²y on the right side. Since both terms involve y raised to the power of 1, the equation is linear.

Therefore, the given differential equation, e*. dx + 3y = x²y, is both separable and linear.

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