Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. y- lny= x^2+1 , dy/dx= 2xy/y-1

See explanation below

Step-by-step explanation:

Given the expression

y- lny= x^2+1

Differentiate implicitly with respect to x

dy/dx - 1/y dy/dx = 2x+0

Factor out dy/dx

dy/dx (1 - 1/y) = 2x

dy/dx (y-1/y) =2x

Cross multiply

dy/dx (y-1) = 2xy

Divide both sides by y-1

dy/dx (y-1)/y-1 = 2xy/y-1

dy/dx = 2xy/y-1

Hence the given relation is an implicit solution to the given differential equation

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints