# Which of the following is an example of a separable differential equation?

## Which of the following is an example of a separable differential equation?

Separable Differential Equations Examples Since the given differential equation can be written as dy/dx = f(x) g(y), where f(x) = x + 3 and g(y) = y -7, therefore it is a separable differential equation. Answer: y’ = xy – 21 + 3y – 7x is a separable differential equation.

What it means for a differential equation to be separable?

Definition: Separable Differential Equations. A separable differential equation is any equation that can be written in the form. y′=f(x)g(y). The term ‘separable’ refers to the fact that the right-hand side of Equation 8.3.1 can be separated into a function of x times a function of y.

What is the first step in solving a separable differential equation?

Steps To Solve a Separable Differential Equation

1. Get all the y’s on the left hand side of the equation and all of the x’s on the right hand side.
2. Integrate both sides.
3. Plug in the given values to find the constant of integration (C)
4. Solve for y.

### Which differential equation is not separable?

y = y sin(x − y) It is not separable. The solutions of y sin(x−y) = 0 are y = 0 and x−y = nπ for any integer n. The solution y = x−nπ is non-constant, therefore the equation cannot be separable.

Is dy dx xy separable?

So something like dy/dx = x + y is not separable, but dy/dx = y + xy is separable, because we can factor the y out of the terms on the right-hand side, then divide both sides by y.

How do you solve a separable equation?

The method for solving separable equations can therefore be summarized as follows: Separate the variables and integrate.

1. Example 1: Solve the equation 2 y dy = ( x 2 + 1) dx.
2. Example 2: Solve the equation.
3. Example 3: Solve the IVP.
4. Example 4: Find all solutions of the differential equation ( x 2 – 1) y 3 dx + x 2 dy = 0.

#### How do you prove a differential equation is separable?

Note that in order for a differential equation to be separable all the y ‘s in the differential equation must be multiplied by the derivative and all the x ‘s in the differential equation must be on the other side of the equal sign.

How do you separate XY?

Three Steps:

1. Step 1 Move all the y terms (including dy) to one side of the equation and all the x terms (including dx) to the other side.
2. Step 2 Integrate one side with respect to y and the other side with respect to x. Don’t forget “+ C” (the constant of integration).
3. Step 3 Simplify.

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