PULUI Consider the following first order differential equation dy 6x?y + = g(x) dx x +...
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
Consider the following differential equation. (x2 − 4) dy dx + 4y = (x + 2)2 Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...
Consider the equation 2xy (y dx + x dy) = (y dx - xdy) sin - Is the equation exact? If not, find an integrating factor, and solve the equation that is exact with the integrating factor
[8] 2. Consider the differential equation dx + (1 - sin(v)) dy = 0 Determine if the equation is exact. If so, solve. If not determine an approximation integrating acco the equation exact. Verify that the new equation is exact, and solve the differential equation using the integrating factor you have found. (Hint: the integrating factor should be a function of y only.)
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
(2) [Problem 1.9.25 Part 1] Determine the integrating factor for the following differential equation. æży dx + y(x3 +e-34 sin y)dy = 0 (3) [Problem 1.9.25 Part 2] Use the integrating factor found in the previous prob- lem to solve the differential equation xạy dx + y(x3 +e-34 sin y)dy = 0.
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x sin(xy))dy Note: Do not use square brackets in your response, use normal parantheses if you have to, i.e "0" Then aM ду and ƏN ax Is this equation exact? Yes No Consider the differential equation: sin(x)dx + 5y cos(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. On=e-54 On=tan(x) Ju=e-542/2 On =...
For the following differential equation: (x^3)dy/dx+y^4+3=0 where dy/dx is the first derivative of y with respect to x, () means power. The equation has initial values y=2.00 at x=1.00 Using Euler method with a step in the x direction of h=0.30: Show the equation to use to generate values of (2 marks) Calculate the missing values of y in the table below I .1.30 1.00 2.00 1.60 For (2 marks)
2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. =- X