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

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

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