Question

In Problemsandverify that the indicated expression is an implicit solution of the given first-order differential equation. Find atleast one explicit solutionin each case. Use a graphing utility to obtain the graph of an explicit solution. Give an intervalof definition of each solution.

Short answer

Answer:

is an explicit solution of the given differential equation and the intervalis.

Step-by-step solution

Step by Step solution:Step 1: Define an explicit function.

In explicit solution unknown functions (dependable variables) is indicated (expressed) in terms of undependable variable and constants. This is known as “explicit solution”.

Let the expression be.

Divideon both sides of the equation.

Determine the derivative of the function.

Let the first derivative of the above function is

Determine the explicit solution.

Substituteandin the left-hand side of the differential equation.

That is same as the right-hand side of the differential equation. The indicated function is an explicit solution of the given differential equation.

Determine the graph of the solution.

Hence the interval of the solution is.

Solve the implicit function.

Using the quadratic formula,.

Here,.

Let the graph of the expression be,