Verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; y = 1/(16 − x2)

Answer with Step-by-step explanation:

We are given that a differential equation

and

We have to verify that the function y= is an explicit function of the given first order differential equation.

Differentiate w.r.t x

By using the formula

Substitute the value of y in given differential equation

LHS=RHS

Hence, the function y is an explicit function of the given first order differential equation.

step-by-step explanation:

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.