Utilize the Separation of Variables Calculator to solve differential equations by entering the relevant details.

Separation of Variables Calculation Formula

The separation of variables is a method used to solve differential equations by separating the variables into two sides of the equation.

dy/dx = g(x)h(y)

By separating the variables, we can write the equation as follows:

dy/h(y) = g(x)dx

Integrating both sides gives us:

∫1/h(y) dy = ∫g(x) dx

Variables:

  • dy/dx is the derivative of y with respect to x
  • g(x) and h(y) are functions of x and y, respectively

To solve the differential equation using separation of variables, follow these steps:

Steps to Solve Differential Equations

The following steps outline how to use the separation of variables method to solve a differential equation.

  1. Write the differential equation in the form dy/dx = g(x)h(y).
  2. Separate the variables to get 1/h(y) dy = g(x) dx.
  3. Integrate both sides to find the solution.
  4. Apply initial or boundary conditions to find the particular solution.
  5. Verify the solution by substituting it back into the original differential equation.