In each of 1 through 6, state whether the given boundary value problem is homogeneous or nonhomogeneousy+ 4y = 0, y(1) = 0, y(1) = 0

L20 - 2 Implicit Diﬀerentiation requires the Chain Rule. Consider the following examples: d (x)= dx d 2 dx (x )= Now suppose that y is a diﬀerentiable function of x. d (y )= dy What is d (y ) dx To Diﬀerentiate Implicitly: Assume y is a diﬀerentiable function of x. 1. Diﬀerentiate both sides of the equation with respect to x. dy 2. Collect all terms involvidx on one side. 3. Rewrite by factoring outy . dx dy 4. Solve for . dx