QUESTION 1 Consider the following differential equation for a function x = x (t): dx dt Using an integrating factor, or otherwise, determine which of the following functions gives the general solution to this equation. A. x = 4t x = e - e OB. x = Ce C.x = 4t D.x = Ce 3t 4t Cet+e - 4t 3t - e where C is an arbitrary constant of integration. 3t - - e 4x = e 3t - 3t where C is an arbitrary constant of integration. where C is an arbitrary constant of integration.

Q: 2y (y² - x) dy dx

A: We know that for the differential equation  Mdx+Ndy=0 if 1M∂M∂y-∂N∂x=fy then the integrating…

Q: The differential equation for which sin¬ x + sin¯ y = C is given by V1- x²dx + /1- y² dy = 0 b. V1-…

A:

Q: The order of the differential equation d (D®y + D® sin æ) = sin æ dx O 5 6 O 7 O 4

A: In this question we have to find order of differential equation.

Q: Find the differential equation of dy 2y-y dx X-y

A:

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

A:

Q: . Find an integrating factor for the differential equation given below that will help you solve it…

A: Use the integrating factor formula

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: What is the integrating factor of the given differential equation (2xy- 1) da + a dy = 0 ? O r-1 O e…

A: The given problem is to find the integrating factor for the given differential equation, we have to…

Q: A heat source is applied to a metal surface, causing the temperature of the metal to increase with…

A: The correct answer is:b) dT/dt = c(T + To) Here's the explanation:dT/dt: This represents the rate of…

Q: Find the integrating factor (I.F.) for a differential equation (3r²y- 2xy + y' ) dx +(-x² - y² )dy =…

A: Compare with exact differential then solve

Q: erential equation: an y = x2. If y(0) e value (corrected up fy(1)?

A:

Q: dy dx For the first order differential equation + 2xy = sin(x), what a the coefficient functions…

A:

Q: Find the general solution to the differential equation x2+3xy+x(dy/dx)=0   The integrating factor…

A:

Q: Use an integrating factor to find the general solution to the linear differential equation dy + dx x…

A:

Q: dI + 501 = 5; where I(0) = 0. dt

A:

Q: y' = 3 t2 y( 1 + t³)

A:

Q: The complementary function (C.F.) of the differential equation:(D² +3?)y=cos lz s. O ge* + cz sin 3z…

A:

Q: dy Given the differential equation -x²y4 +xy=x*. The degree of this differential equation is dx 40 2…

A:

Q: Determine the type of differential equation given below: * 2x(у + 1)dx — уdx %3D 0

A: Given differential equation  2x(y+1)dy - ydx = 0 If the differential equation is in the form…

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A:

Q: dT Write a differential equation of the form = f'(t) (for instance, = -k(T - A) or dx dt dt kP) that…

A: The differential equation that represents the described situation is:  ⇒      dPdt = k × P

Q: dy +y cotx = cscx is dx The integrating factor for the differential equation %3D Select one: cotx…

A:

Q: dx dt dT dP = = f'(t) (for instance, = -k(T - A) or dt dt Write a differential equation of the form…

A: To write a differential equation of the form dxdt = f'(t) that is a mathematical model of the…

Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

Q: A differential equation is a linear DE in y if it is 1st order in y it is 1st degree in y and all…

A: