General solution

Find the general solution, if possible. Otherwise find a relation that defines the solutions implicitly: xy' - y=2y(ln y - ln x)

Relations

Find the general solution, if possible. Otherwise find a relation that defines the solutions implicitly: xy' - y=x(1 + e^(-y/x))

Exact equations

First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly: [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

Integrating factors

Using: d tan^-1 (x/y)=(y dx - x dy)/(x^2 + y^2), and ½ d ln(x^2 + y^2)=(x dx + y dy)/(x^2 + y^2) find integrating factors for, and solve, the following equation: (2x^(2)y + 2y^3 - x) (dy/dx) + y=0

Dependent variables

Find a new dependent variable such that the equation becomes linear in that variable. Then solve the equation: 1/(y^2 + 1) y' + 2/x tan^-1 y =2/x

Domain

State the largest possible domain of definition of the given function f: f(x, y)= square root of(4 - x^2 - y^2)

Graph

Describe the graph of the function f: f(x, y)= - (36 - 4x^2 - 9y^2) : is the square root of

Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. The dimensions of a closed rectangular box are found by measurement to be 10 cm by 15 cm by 20 cm, but there is a possible error of 0.1 cm in each. Use differentials to estimate the maximum resulting error in computing the total surface area ...continues

Chain rule

Write chain rule formulas giving the partial derivative of the dependent variable p with respect to each independent variable: p=f(x, y, z); x=x(u, v), y=y(u, v), z=z(u, v)

Gradient vector

Find the gradient vector f at the indicated point P: f(x, y, z)=(x^2 + y^2 + z^2) ; P(17, 3, 2) : is the square root of