Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) A. For each of the following, indicate the dependent and independent variables, classify as an Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), give the order, the degree, and. Also indicate whether the equation is linear and non-linear. 2. 4xq' + e²xq = 0

Q: what is rational function ?

A: Relational number Our connection is number three. As you'll see that number is specific to our…

Q: Evaluate the integral π/ 10 S 3cos 5t sin 5t dt. 0

A: Please see the below picture for detailed solution.

Q: Which of the equations below is a second order nonlinear differential equation? A. B. D. E. 2 x²y-…

A:

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A: To find the value of C

Q: Question 16 Eliminate the arbitrary constants of y=c₁e³+₂x4-sin 3x

A: We are given a differential equation,  y = c1ex +c2x4 -sin3x   ... @ We havet o eliminate arbitrary…

Q: 4. Find the limit. lim x-0 lim X-0 5+5x+ sin x 6 cos x 5+ 5x + sin x 6 cos x CA. Yes, lim f(x)…

A:

Q: The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35…

A: Here assume P(t) be the population of world in billions at any time t in years

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. ey O eLny °A O D.Y O…

A: given    y(x+y+1)dx+x(x+3y+2)=0

Q: Graph the following equations and explain why they are notgraphs of functions of x.a. |x| + |y |= 1…

A: Given data:- (a);  x+y=1 (b); x+y=1

Q: Which of the following equations is NOT an exact equation?

A:

Q: Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population…

A: a) Assuming that the size of the fish population satisfies the logistic equationdPdt=rP1-PN

Q: A baseball diamond is in the shape of a square with 50 ft sides. How far is it from home plate to…

A: A baseball diamond is in the shape of as quare with 50 ft sides. To determine how far is it from…

Q: Which of the following statement is TRUE? 8:01 AM A. An ordinary differential equation (ODE)…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: For the function f(x) = 5x² 2x, evaluate and simplif f(x+h)-f(x) h 11

A: f(x)=5x2-2x hence f(x+h)=5x+h2-2x+hf(x+h)=5x2+5h2+10xh-2x-2h

Q: What is a suitable integrating factor that can be used to solve the equation dy x + 2y - 4xy - e-*…

A:

Q: The integrating factor (IF) of the equation y' - 2ycot2x OA. sin2x O B. cot2x = 1-2xcot2x - 2csc2x

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

Q: Graph the functions in Exercises 25-28. (x, 25. f(x) 12 X, 11 S1/x, 28. G(x) =

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: dy What is the IF for solving the linear equation: x + dx OA. O B. O D. O E. 3 N/W X2 C. 3 3x 2 3/2…

A: Topic- differential equations we are given, xdydx+3y2=cos x,x>0wew know thaty'+Py=Q is a form of…

Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: 1. Given that lim f(x) = -1 and lim g(x) = 8, find the following limits. H-3 →3 f(x)5 +3 (b) lim -3…

A:

Q: This problem tests calculating new functions from old ones: From the table below calculate the…

A:

Q: What is the integrating factor of (1+x)y +2y= 21ax sin.x 1+x

A:

Q: 38. Critical Thinking How many students receive each grade? Each student receives a grade of A, B,…

A:

Q: dy Solve for the value of C in the equation: + ycotx = 5ecosx when y() = 1 dx OA.-5 OB. 5 OC.-4 OD.4…

A: It is a linear differential equation of first order so find first integrating factor

Q: What is a suitable integrating factor that can be used to solve the equation dy cos(2x) = 0 O A. OB.…

A: To determine the suitable integrating factor that can be used to solve the equation.xdydx+2y-4xy-e-x…

Q: Which of the following is a non-homogeneous function? O tan³y/x xLnx − xlny x³ − xy + y² 3 2 - (y² +…

A: function f(x, y), if it can be written  by writing x = kx, and y = ky to form a new function f(kx,…

Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: 1) Using the definition, calculate the derivatives of the functions. Then find the values of the…

A: Solve by derivatives

Q: Which of the following equations can be made into a linear differential equation? A. (x² + xy)dy -…

A: To check: Which of the given differential equations is linear?

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Given, dy/dt = 5t4-3et+2 And conditions y= 1  and t=-2

Q: † (OM_ON) - . If = -3, O A. e5 U O E. e-5 y5 y -5 then what is the integrating factor? None of the…

A:

Q: Which of the following is TRUE about the differential equation x- dx O A. The equation is…

A: We have to find form of given differential equation.

Q: Which of the following equations is NOT a variable separable differential equation? O A. 2xydx + (x²…

A: Option D is not a variable  separable  differential  equation .

Q: ple of gas is compressed at a constant temperature, the pressure P of the gas is inversely…

A: Pressure is inversely proportional to volume , take k as constant   for P = 50 kpa , and V = 0.103…

Q: Evaluate the following integral. π/4 S 0 cos x)² dx secx+cOS X)

A: Explanation of the answer is as follows

Q: Which of the equations below is a second order nonlinear differential equation? A. 2 x²y - (1 - dx)²…

A: To find the nonlinear equations.

Q: Find y'(x). y'(x) = y = √-1 + 2x At what point on the given curve is the tangent line perpendicular…

A: Given query is to find the derivative and the point where slope of tangent is perpendicular to the…

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4e³ − x²y² – 3x)dy = 0 when…

A:

Q: dy 3y What is the IF for solving the linear equation: x + = dx COSX,x>0

A: The given differential equation, xdydx+3y2=cosx, x>0 We have to find the integrating factor

Q: If f(x) = f'(x) = f'(2) = tan x 2 sec x 1 + 2 tan(x) sec(x)

A:

Q: 1. Find the limit. lim X-5 lim x-5 2 √x +11 -6 x-5 2 √√x+11 -6 X-5 =

A:

Q: Which of the equations below is a second order nonlinear differential equation? O B. O A. 2 dy |x²y…

A:

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A:

Q: Question 26 Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x =…

A:

Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D. 4 E. None of the Choices dy dx…

A: Find integrating factor of linear differential equation

Q: Let f(x) f'(x) = 2 cos x + 7 tan x 2 sin(x) + 7 sec²(x) 1' (5) = 6

A:

Q: 5 5 3 Suppose ff(x) dx = 25, f f(x) dx = 10, f g(x)dx = 10 and h(x) = = 3 0 0 the following: 0 b.…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

A: Given query is to apply sine law and complete the triangle.