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in this video were going to focus on solving differential equations by means of separating variables so lets start with this example problem d y d x is equal to x squared divided by y squared now in this problem what we need to do is separate the variables on one side we only want to have y variables and on the other side of the equation we only want to have x variables so since we have a fraction separated by an equal sign lets cross multiply d y times y squared is simply y squared d y and on the other side its going to be x squared dx now that weve separated the variables we can integrate both sides of the function the antiderivative of y squared is y cubed divided by 3. the anti-derivative of x squared is x cubed divided by 3 and on one side of the equation we need to add a constant c so now lets get y by itself so lets multiply both sides of the equation by three so its going to be y cubed is equal to x cubed plus 3c now 3c is a constant so we can just write c for the tota
