41-50. Differentials Consider the following functions and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x) dx. 41. f(x) — 2х + 1 42. f(x) = sin? x %3D 43. f(x) = 1/x 44. f(x) = e2* 45. f(x) = 2 - a cos x, a constant 46. f(x) — (4 + х)/(4 — х) 47. f(х) — Зх3 — 4х 48. f(x) — sin х 49. f(x) = tanx 50. f(x) — In (1 — х)

Q: 1. Consider the differential equation dx = 3x(y – 1)2. Let y = f(x) be the particular solution to…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: consider the differential equation dy/dx=sinx/y, for which the solution is y=f(x). Let f(0)=1. Which…

A:

Q: Given the differential equation y" – y' - 2 = tan x. Find the Wronskian. a. W = e* b. W = 2e* c. W =…

A:

Q: 4.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it.…

A: To tell which of them are exact differential equation.

Q: 1. Find the order and degree of the differential equation C. 9th order, 13th degree 3rd order, 7th…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 8. consider the differential equation x*y3 + x(1 + y²) = 0 Which of the following integration factor…

A: Integrating factor is not unique. So check the correct option by multiplying the given differential…

Q: Q.3.a).lf « & ß are real numbers, ß # 0 then the function y, = e" cos ßx and y, = etr sin ßx are…

A: Give two real numbers α,β≠0. First we have to check the linear independence of…

Q: Using Picard's method to obtain y for x = 0-1 to 0-5 for the differential equation dy %3D =1+xy with…

A:

Q: 11. If the following differential equation has to be transformed to a separable form by substituion.…

A: According to guidelines we solve only one question. Please repost remaining questions to get…

Q: (a) For what values of k does the function y = cos(kt) satisfy the differential equation 10oy" =…

A: Given function is y=coskt To find value of k such that 100y"=-49y Solution: Differentiating the…

Q: X- = y Consider the following differential equation. dx y Let f(x, y) Find the derivative of f. %3D…

A:

Q: sec y Obtain the solution of the differential equation y' x-4x+5 a. 2 sin y = In(x² – 4x + 5) + C b.…

A: ∫cosx=sinx +c∫dx1+x2=tan-1(x)+cCosx=1secx Given D.E y'=sec(y)/x^2-4x+5

Q: dfix) ta fræ) =b dx fac) (- e a

A: Given:     df(x)dx+af(x)=b

Q: 1. Given the following differential equations (DE): A. e*y' = x – 2y B. y' – ey = sin x Identify if…

A: Given:-A exy1 = x-2yB y1-ey = 8in(x)To find:- identify following D.E. are linear ODE or non-linear…

Q: Consider the following differential equation as an exact differential equation. Find the value of P.…

A:

Q: (3) Consider the differential equation (x+ sin y) dx + (x cos y – 2y) dy = 0 (a) Determine whether…

A:

Q: 3. The differential equation of the family of curves whose equation is y = x° + ax +bx + 5 given by…

A:

Q: Find a function y = y(x) that has all of the following properties: • It satisfies the differential…

A:

Q: 3. Identify either the following equation if it is differential equation (DE) or not. If it is a DE…

A:

Q: An industrial process creates a chemical L. At time t hours after the Start of the process the…

A:

Q: dy What is the general solution to the differential equation cos(x) dr cos(x) +1 COS…

A:

Q: 4. Consider the differential equation dx dy = xy. Let y = f(x) be the function that satisfies the…

A:

Q: Consider the following differential equation. dy - y = x2 sin(x) dx dy + P(x)y = f(x). dx Find the…

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

Q: Ive the differential equation x - 2y) dx + (y In (y - x)² + (x b. In (y - x)² + (x 1) dy = 0 1) + 2…

A:

Q: (iv) The trial form y,(x) for the differential equation y" + 2y' + 2y = cos(x) is... (a) yp(x) =…

A:

Q: rove that the given first order ordinary differential equation (2x – y) dx – (x – 2y) dy = 0 is an…

A: compare differential equation with Mdx+Ndy=0 if ∂M∂y=∂N∂x then DE is exact

Q: 1) For the differential equation = e-(2 + cos(x)) dy i) Find the solution satisfying y(0) = 3. Find…

A:

Q: 1. Consider the differential equation: (x cos y) dy + (x + 3x sin y) dx = 0. (a) Show that this…

A:

Q: I. Given differential equation d'x tanh (xr") 17/68 1. Determine its order. 2. Determine its degree.…

A:

Q: How does the following differential equation y dr + x dy = 0 satisfy the criterion for an exact…

A:

Q: 6. Find the general solution of the following differential equation. Primes denote derivatives with…

A:

Q: (3) Consider the differential equation (x + sin y) dx + (x cos y – 2y) dy = 0 : COS (a) Determine…

A:

Q: 16. For the differential equation x^2 dx - (y+1) dy = 0, find the value of x when y=2 if y(0)=1. %3D…

A: topic - differential equations

Q: 1. What is the best method to use given a differential equation with f(x) = sec x? A. Method of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1 Indicated a definition interval solution of the given differential equation dy + y = x + 1 dx f(x)…

A:

Q: The non-exact differential (x² + y²)dx + (3xy² + 2xy + x³)dy = 0 can be reduced to exact after…

A:

Q: Find a function y = y(x) that has all of the following properties: • It satisfies the differential…

A: We have to find a function y=y(x) that has the following properties. 1) It satisfies the…

Q: (20) The concentration c of glucose in the blood with respect to time t is given by the differential…

A:

Q: 3. Find the function M(x, y) such that M(x, 0) = e¯ª and the differential equation M(x,y) dx + (sin…

A:

Q: SLOVE 11. Differential equation: dr = -ti – tj – tk dt Initial condition: r(0) = i + 2j + 3k

A:

Q: Consider the following differential equation as an exact differential equation. Find the value of P.…

A:

Q: Discuss how the functions M(x, y) and N(x, y) can be found so that each differential equation is…

A: To find the solution of given equations

Q: 3) Consider the differential equation (x + sin y) dx + (x cos y – 2y) (a) Determine whether the…

A:

Q: (-2e* sin(y) – 4y)dx + (-4x – 2e* cos(y))dy=0 Use the exact differential method to find a function…

A: The given differential equation is: -2ex sin y-4ydx+-4x-2ex cos y dy=0

Q: 4. Find the general solution of the following differential equation given that y(1) = 10 [Hint:…

A: 4 Given differential equation is x+1dydx+y=lnx...1. We have to find general solution of the given…

Q: 3. Let the function y = y(x) satisfy the equation (y – x)² = 1 + 3(y +æ)*. Show by implicit…

A:

Q: 11) Consider the differential equation: xy'/(x5+9)y = cos(x) + e6x/y. Put the differential equation…

A: Here given differential equation as

Q: 5) Find the differential equation of family of circles through the intersection of the circle x2 +…

A:

Q: Compute y' and y". The symbols C, and C, represent constants. y = C,e sin x + C,ex cos x y'(x) =…

A: