A differential equation of the form dy dx f(x, y) is called separable if 2025

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  1. Click ‘Get Form’ to open it in the editor.
  2. Begin by identifying the components of the differential equation. Look for the function f(x, y) and ensure it can be expressed as a product of two functions φ1(x) and φ2(y).
  3. Rewrite the equation in separable form: dy = φ1(x)φ2(y) dx. This will help you separate variables for integration.
  4. Integrate both sides of the equation. Use our platform's tools to input your integrals clearly, ensuring that you maintain proper notation.
  5. After integration, express your solution in implicit form F(y(x)) = G(x) + C. This step may require careful manipulation of your integrated results.
  6. If applicable, solve for specific initial conditions by substituting values into your general solution to find particular solutions.

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Separable differential equations are a special type of differential equations where the variables involved can be separated to find the solution of the equation. Separable differential equations can be written in the form dy/dx = f(x) g(y), where x and y are the variables and are explicitly separated from each other.
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.
If we can write our DE in the form dy/dx = f(x) * g(y), it is called separable.
What are Separable Differential Equations in Calculus? Differential equations in which the variables can be separated from each other are called separable differential equations. A general form to write separable differential equations is dy/dx = f(x) g(y), where the variables x and y can be separated from each other.
Calc II is a bear of a class. Diff Eq isnt as bad but make sure you select a good professor for it. It can be a bear of a class if you pick the wrong professor (as opposed to Calc II, which is difficult even with the best professors).