https://youtu.be/jVVTmkfBe48

In this video I go over another example on solving separable equations and this time look at the differential equation: dy/dx = 6x<sup>2</sup>/(2y + cosy). In this particular example, determining the solution explicitly in terms of y as a function of x is actually impossible so the best that we can do is solve it implicitly, that is an equation that contains y and x but no derivatives. But luckily, there are many computer algebra systems and calculators that can still graph solutions to implicit equations. One of them is https://kevinmehall.net/p/equationexplorer/ and I suggest you check it out because it is a very cool and powerful online graphing calculator!

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# Differential Equations: Separable Equations: Example 2

**Example:**

Solve the differential equation:

![](https://cdn.steemitimages.com/DQmNXaxj5V4nrWMeE3GoaciH8aUUQ9YH5E87HDtjDG57KqH/image.png)

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**Solution**

![](https://cdn.steemitimages.com/DQmVAjWk4cb6FcdUhbgZV38JC4pJRHnsGbiNcdFXD1B1u7H/image.png)

This equation gives the general solution implicitly.

In fact, it's impossible to solve this equation to express y explicitly as a function of x.

Some computer algebra systems can plot curves defined by implicit equations.

The graph below shows several solutions, corresponding to different values of the constant C.

![](https://cdn.steemitimages.com/DQmRb9ZwYque8fF72d4tByatYfgoJkGj7sRtRjrCjUTSN13/image.png)

Graph produced from: https://kevinmehall.net/p/equationexplorer/