### Differential Equations

For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous. a) df/dx +f^2=0 (See attachment for all questions)

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous. a) df/dx +f^2=0 (See attachment for all questions)

Consider the vector field F(x,y)= (-yi+xj)/(x^2+y^2) Question1)Show that F is the gradient of the polar angle function teta(x,y)=arctan(y/x) defined over the right half-plane x>0 . Question2)Suppose that C is a smooth curve in the right half-plane x>0 joining two points : A:(x1,y1) and B(x2,y2).Express "integral(F.dr)"on

A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. If the pool is being filled at a rate of 0.8 ft^3/min, how fast is the water level rising when the depth at the deepest point is 5 ft?

A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at a rate of 0.2 m^3/min, how fast is the water level rising when the water is 30 cm deep?

A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 12 ft^3/min, how fast is the water level rising when the water is 6 inches deep?

Differential Calculus The Equation of a Tangent

Let x = (1/2)(u^2-v^2), y=uv, and f=f(x,y) [QUESTION 1] use the chain rule to derive the change of variables formula in matrix form: (fu,fv)=A*(fx,fy) {actually it is vertical , so fu is at the top and fv is at the bottom. Same for fx and fy: fx is under fy; sorry for the notation I cant do it another way} [QUESTION 2]

Consider the function : f(x,y) = x(x-1)(x-2) + (y-1)(x-y) [QUESTION 1]find the maximum and the minim values of the directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies . ( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the directi

Consider a triangle in the plane, with angles , a, b , c. Assume that the radius of its circle is equal to 1. 1) by decomposing the triangle into six right triangles having the incenter as a common vertex, express the area A of the triangle in term of a, b , c ( the answer should be a symmetric expression). Then use the resu

A population obeys the logistic model. It satisfies the equation dP/dt = 2/1300 P(13-P) for P>0 Assume P(0)= 3 Find P(74)

Find the General Solution of the equations. (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0

1. Find all the critical numbers: . 2. Find all the extrema in the interval [0,2 ] for . 3. Find the absolute maximum and the absolute minimum on the interval (1,4]. 4. State why Rolle's Theorem does not apply to the function on the interval [-2,0]. 5. Find all relative extrema of , include the designation of maxim

Show that equation is of exponential order and not of exponential Order. (please see attachment for details)

Before starting, the answer to the 2nd problem is NOT y=3.9x+20 or y=4.1x-300. Those are the solutions to the first part of the question. The second part is asking for the TOTAL cost when you have "x" amount of feet, not just the cost of digging ONE foot. I posted earlier and received the above answers. The question I would like

What are the domain and range and x intercepts of the function? Approximate to two decimal places. y=-x^2-20x-3

Please respond with a Microsoft Word document. Thank you. Please see attachment for actual questions and full formulas. 1. Decide whether Rolle's Theorem can be applied to on the interval [-1,3]. If Rolle's Theorem can be applied, find all the values, c, in the interval such that . If Rolle's Theorem cannot be a

Please respond with a Microsoft Word document with the answers written in standard text. Thank you. Series of Various Calculour Questions Attached. You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please ju

Please see attached

Given that the differential equation y^n + p(x)y' + q(x)y =0 has two solutions x^2 -x and x^3 - x. Use the Wronskian to find p(x). See attachment for better formula representation.

Determine whether the following questions are linear or nonlinear. (a) yy''-y'=sin(x) (b)x^2y''-y'+y=cos(x)

Attached is more clear 1. Distance from a a point to a curve: Find the shortest distances between the point (1,2,1) and a point on the curve r(t)= (1/t*i)+(lnt(t)*j)+(sqrt(t)*k) 2. Distance from a point to a curve: Find the maxmium distances from the point (1,2,-1) to a point on the curve of intersection of the plane z=(

Solve for variable y in terms of t W/ given initial condition: dy/dt + 4y = 40sin3t y(0)=6

Solve y in terms of t with initial conditions given. a.) (d^2)y/dt^2+3dy/dt+2y=24e^-4t y(0)=10 y'(0)=5 b.) (d^2)y/dt^2+6dy/dt+9y=0 y(0)=10 y'(0)=0

Use the method of undetermined coefficients to solve the following differential equation. y'' + 2y' - 3y = 9x - 10 sin x y(0)=0 y'(0)=4

Y'' + p(x)y' + q(x)y = 0 has two solutions x^2 - x and x^3 - x. Use the Wronskian to find p(x).

The problem is in JPEG, thank you. Quarter horses race a distance of 440 yards (a quarter mile) in a straight line. During a race the following observations where made. The top line gives the time in seconds since the race began and the bottom line gives the distance (in yards) the horse has traveled from the starting line.

The birth rate in a state is 2% per year and the rate is 1.3% per year. The population of the state is now 8,000,000. a) At what rate are babies being born in the state now? with units b) At what rate are people dying in the state now? c) Write a differential equation that the population of the state satisfies. include

Use Stokes' Theorem to evaluate int (F.dr) over C where F = x^2*y i +x/3 j +xy k and C is the curve of intersection of hyperbolic paraboloid z= y^2-x^2 and teh cylinder x^2+y^2=1 oriented counterclockwise.

1. Let f(x,y) = xy + 2x y - 6xy (a) Locate the critical points of f(x,y) and determine if they are local maxima, minima, or neither. (b) Find the first and second order approximations of f(x,y) at the point (1,-1).

A skydiver, weighing 70kg, jumps from an aeroplane at an altitude of 700 metres and falls for (T) seconds before pulling the rip cord of his parachute. A landing is said to gentle if the velocity on impact is no more than the impact velocity of an object dropped from a height of 6 metres. The distance that the skydiver falls d