Please answer all parts, Problem 4-7. Thank you! Problem 4 dy of the following function y...
PLEASE. ANSWER ONLY IN MATHEMATICA, THESE PROBLEMS CAN ONLY BE DONE IN MATHEMATICA. I NEED THEM TO BE DONE STRICTLY IN MATHEMATICA. WILL DOWN VOTEIF NOT DONE IN MATHEMATICA!!!!! (thank you in advance) Lab Exercise 1. Solve: (4xy3 - cos y -e ")dx + (6x2y* +xsin y 3) dy 0 2. Solve the initial value DE: (Cos(x)Sincx)- xy2 )dk + y(l-)dy-0, y(o)-2 3. a. Determine a function M(x y) so that the following DE is exact: Mx, y) dx +(xe+...
Please answer #4 Problem 3: Find a solution to the IVP dy dy + dc2 + y = 0, y(0) = y'(0) = 1. dx Problem 4: Suppose you are given the differential equation ay" +by' + cy = 9(2) where a, b, and c are constants. For each of the following choices of g(x), write down the form for the particular solution Yp that you would use: (a) g(x) = 205 (b) g(x) = x²e32 (c) g(x) = xº...
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures and present it below (12 points): your mumerical result for the ae ust be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The substitution used to solve the differential equation is as follows (mark...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
Please answer #3 Problem 3: Find a solution to the IVP dy dy + dc2 + y = 0, y(0) = y'(0) = 1. dx Problem 4: Suppose you are given the differential equation ay" +by' + cy = 9(2) where a, b, and c are constants. For each of the following choices of g(x), write down the form for the particular solution Yp that you would use: (a) g(x) = 205 (b) g(x) = x²e32 (c) g(x) = xº...
Problem 3: Find a solution to the IVP dy dy + dc2 + y = 0, y(0) = y'(0) = 1. dx Problem 4: Suppose you are given the differential equation ay" +by' + cy = 9(2) where a, b, and c are constants. For each of the following choices of g(x), write down the form for the particular solution Yp that you would use: (a) g(x) = 205 (b) g(x) = x²e32 (c) g(x) = xº cos(x) (d) g(x)...
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
Please answer ALL parts of the question. Will rate immediately!! Thank you!! 3. Modeling with Differential Equations a. Provide slope fields for the following differential equations: DE#1: y'-y-cos x; DE#3: y'-y-cos y. (4pts) DE#2: y-x-cos y, b. For each slope field, draw the solution curve for the initial condition y(0) 1. (4pts) Attach separate pages c. Use Euler's method to estimate y(2), using steps of h 0.5 and h0.1 '-y cosx,y(0)-1 You can use technology. Write your results accurate to...
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
(1 point) All parts of this problem refer to the function below. y=(3+52)5/2 dy a) Use logarithmic differentiation to find dar dy dx b) Find the slope of the tangent line at x = = 1. Slope = C) Find the equation of the tangent line at x = 1. Tangent line: y