Help with differential equations

Question

The rate of change of the revenue R with respect to the number of units X sold of an item, is equal to the double of the cube of the revenue minus the cube of the number of units, all divided by three times the product of the square of the revenue and the number of units sold. Find the relation between the revenue and the number of units sold if R = 0 when x = 10.

Answer 1

OK, first of all: I disagree with Patrick, the R=0 in the denominator goes away because the derivative has R³ in the numerator and R² in the denominator so there is no effective 0 divisor,

I cannot give the whole derivation of the solution here but the hint I gave in my comment gets you the solution and if

you are actually taking a course in differential equations, you should be able to get the solution with that hint. You will get that

x² D_x[z/(x²)] = -x² and the solution is easy from there: R³=100x²-x³.

If when you review this in class, you get a different solution, I would like you to let me know!!