Question

the expression dy/dx = x^3(sqrt(y)) gives the slope at any point on the graph of the function f(x) where f(2) = 8 write an expression for f(x) in terms of x. And what is the domain of f(x)?

Answer 1

here's what I did:

dy* 1/cubert(y) = x dx

integrate both sides

3y/2cubert(y) = x^2/2 + c

solve for c, c = 4

Then I tried to put into y = form, but I'm not sure what to do about the two y's on left side.