Chapter 4 Test Key

Problem 1:

a)

b)

separating the variables:

integrating both sides:

yields:

algebra and squaring both sides:

Checking our work and letting:

Checking if the function f(x) satisfies the original differential equation:

Letting:

Diff = 0, so f(x) is a solution.

c)

separating the variables and integrating:

yields:

solving for the roots:

Letting:

Using just the principle root (since y is specified as + )

graphing domain for the solution function:

Checking if the function f(x) satisfies the original differential equation:

Letting:

Problem 2:

a)

Let:

or

b)

(double angle formula)

using Riemann sums

Problem 3:

which is what the calculus answer gives:

Problem 4:

let:

differentiating:

so...

which agrees with the Mathcad solution of: