Question

13. What is a separable differential equation? How do you solve it?

Short answer

A differential equation is called separable if it can be rewritten in the following form:

\(\frac{{dy}}{{dx}} = f(x) \times g(y)\)

Step-by-step solution

To Find the Differential Equation

A differential equation is called separable if it can be rewritten in the following form:

\(\frac{{dy}}{{dx}} = f(x) \times g(y)\)

Notice how the right-hand side is a product of two expressions, each of which is composed on only one variable.

To solve this differential equation, we will rewrite as shown below:

\(\frac{1}{{g(y)}}dy = f(x)dx\)

Final Answer

After this, we just have to integrate both sides

\(\int {\frac{1}{{g(y)}}} dy = \int f (x)dx\)

A differential equation is called separable if it can be rewritten in the following form:

\(\frac{{dy}}{{dx}} = f(x) \times g(y)\)