First-Order Differential Equations with Separable Variables - Example 1
Over the next few posts, we'll start expanding the idea behind first-order differential equations with separable variables. Basically, if we are able to express a differential equation in the form of...
...that is, a function of x, F(x) by a function of y, G(y) - we can then isolate all of the y's on the left-hand side of the equation and all of the x's on the right hand side of the equation, i.e.:
And we can then integrate both sides of the equation to find a general solution to the function y(x).
Ok. Let's have a look at an example. Let's find the solution to...
First, we can separate the variables by factorising x on the right-hand side...
...and segregate the y's and x's to the left- and right-hand sides of the equation respectively, and subsequently, integrate both sides...
So we have an implicit solution. To get an explicit solution, we simply need to make y(x) the subject.
If you need a clearer explanation, play my video below...
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How do you do the math typesetting here?
They look like LaTeX fonts. How do you incorporate LaTex in steemit?
@homes showed me how to do this. I use the webpage www.quicklatex.com, which generates the latex equations as PNG images. I then just insert those images into the post. :)
Thank you for the hint.
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