In this video I go over another example on solving separable equations and this time look at the differential equation: dy/dx = 6x2/(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:
Solution
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.
Graph produced from: https://kevinmehall.net/p/equationexplorer/