Question

The solution of the Bernoulli's differential equation y' - y{ x = y² is

Select the correct answer.
a. y = (cx-xlnx)
b.y = 1/(cx-xlnx)
c. y = 1 + ce*
d.y = c{x-x/2
e.y = 1/(c/x-x/2)

Answer 1

The solution to the Bernoulli's differential equation y' - xy = y² involves transforming it into a linear equation through a substitution and then solving for y as a function of x. Option b, y = 1 / (cx - xlnx), reflects the typical solution form to such an equation.

Step-by-step explanation:

The Bernoulli's differential equation presented here is y' - xy = y². Solving this type of differential equation involves a transformation to a linear differential equation through the substitution v = y⁻¹. We then can solve the linear equation to find v as a function of x, and consequently, y as a function of x.

The correct solution format for a Bernoulli's differential equation can often be represented as y = 1 / (cx + g(x)), where c is a constant and g(x) is a function of x. Without solving the entire equation, based on the typical solution form for a Bernoulli equation, we could infer that the solution would look similar to option b. y = 1 / (cx - xlnx).