The dynamic equilibrium of a one-story building is described by the following equation: x(t) = x.(t) + X(t) where x(t) = displacement in meters, t= time in seconds, x.(t) = e-0.4[A cost + B sin t], is the complementary function, and X(t) is the particular integral (a) Determine the homogeneous second-order DE, assuming X(t) = 0. (b) Determine the non-homogeneous second-order DE, assuming X(t) = 10. (c) Determine the particular solution of the DE in (b) assuming x(0) = 0, and x'(0) = 0.

Q: Find and sketch the domain of the functions of two variables: 1. f(x, y) = = 16x² - y² x + 3y

A: The given function is  fx, y=16-x2-y2x+3y We have to find and sketch the domain of the given…

Q: A. . Find the derivative of the function at Po in direction of A. g(x,y) = x- + V3sec (2xy), Po (1,…

A: We know that; The expression for the directional derivative of the function g in the direction of A…

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

A:

Q: The temperature distribution u(x, t) in a bar 1 m long, insulated along its length, is given by the…

A:

Q: Find y as a function of t if y (0) = 7, y'(0) = 3. y(t) = 25y" +50y + 106y = 0,

A:

Q: Find a linear approximation to f(x,y) : = (x? + y²)e-(x²+y*). At (0, 0), and use it to approximate…

A:

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: The minimum rate of change of the function f(x, y) = In(x² + y²) at the point (-1,0) is: a. -1 O b.…

A:

Q: Determine the required integrating factor: y dx = (ye-2x) dy Oy² O e¹ ОУ 2e."

A:

Q: There is a tank in the shape of a paraboloid:   Water is being pumped into the tank at a constant…

A: Water is being pumped into the tank at a constant rate of 2π cubic inches per minute. If y denotes…

Q: . Using Bisection Method solve for the oot of f(x) = e¯x(x² + 5x + 2) + 1, [-1,0]

A:

Q: Consider z = f(x,y) = x2 + 3xy + e2y. Find the equation of the tangent when x = 1 and y = 0.   Find…

A:

Q: dw Jse the chain rule to find dt where w-x+y,x sint + cost y = cost- sint.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.