How to Solve Separable Differential Equation
Separable differential equations can be easily solved using the steps discussed below,
- Step 1: Arrange the given differential equation, in the form, dy/dx = f(x) g(y).
- Step 2: Separate the dependent and the independent variable on either side of the equal sign. As, dy/g(y) = d(x)f(x).
- Step 3: Integrating both sides individually to get the required solution ∫dy/g(y) = ∫ f(x) dx.
This can be understood with the example discussed below,
Example: Solve dy/dx = x3/y2.
Solution:
Given DE, dy/dx = x3/y2
⇒ dy(y2) = x3(dx)
Integrating both sides
∫dy(y2) = ∫x3(dx)
⇒ y2+1/(2+1) = x3+1/(3+1) + c
⇒ y3/3 = x4/4 + c
This is the solution to the given differential equation.
Separable Differential Equations
Separable differential equations are a special type of ordinary differential equation (ODE) that can be solved by separating the variables and integrating each side separately. Any differential equation that can be written in form of y’ = f(x).g(y), is called a separable differential equation.
Basic form of the Separable differential equations is dy/dx = f(x) g(y), where x is the independent variable and y is the dependent variable.
Table of Content
- Standard form of Separable Differential Equation
- What is Separable Differential Equation?
- How to Solve Separable Differential Equations
- Initial Value Problem on Separable Differential Equations
- Examples on Separable Differential Equations
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