If an equation relating the independent variable x and the dependent vari-

able y can be solved for y in the form

yf (x),

with f(x ) a function of x , the equation is said to be solvable explicitly for y. However, the complexity of many equations is such that an explicit solution

for y is impossible to obtain, yet given x , y can be found by numerical means.

When this occurs the equation is said to define y implicitly in terms of x .

Thus, for example, the equation