Find the position function x(t) of a moving particle with the given acceleration a(t), initial position x, =x(0), and initial velocity vo = v(0). a(t) = 3 v(0) = 0, x(0) = 0 (t+ 3)4

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A:

Q: Find a homogeneous LDE with constant coefficients that has y=e+ 2e-x as a particular solution.

A: Homogeneous LDE with constant coefficient :   A Linear differential equation with constant…

Q: The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground…

A:

Q: Q1: Use Newton - Raphson method to estimate the 3 Yoot of fcx) = X- X - 1 , employing an initial %3D…

A: To find the root of fx=x3-x-1 by using Newton Raphson method with initial guess of x0=1.

Q: Find the general solution of

A:

Q: Find the initial value for the function f(t)= 2u(t)+3 cos u (t). O 2 O 3 O5

A: Consider the function f(t)=2 u(t) + 3 cos u(t). To find the initial value of this function, use the…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at…

A: The heat equation given is as follows: k∂2u∂x2-hu=∂u∂t, 0<x<L,…

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

A:

Q: yy' – xcos(x²) = 0, y(0) = -2

A: We have to find the particular solution of the given initial value problem.

Q: SOLVE THE PARTIAL DIFFERENTIAL EQUATION BY LAPLACETRANSFORM uz(x, t) + u¿(x,t) = sint given that…

A:

Q: Solve the solution of the DE of the Gompertz function: dP = c ln| dt In[P

A: To solve the given Differential Equations.

Q: Suppose we have a velocity function and an initial condition for position: 1 1 2t v (t) = r (1) =…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

A:

Q: Use the Laplace transform to solve the differential equation, subject to the indicated initial…

A: Here we use basic definition of LP transform

Q: What is the differential equation of the orthogonal trajectories of the family of curves X = Cy? А)…

A:

Q: This is a differential equations problem.

A:

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

A:

Q: b. Using differential equations, find the orthogonal trajectories of the following family of curves:…

A:

Q: Y' + 3Y = 6e-3t cos6t + 24 ; Y(0) = 0,

A: The given IVP is as follows. Y'+3Y=6e-3tcos 6t+24, Y0=0 Apply Laplace transform on both sides of the…

Q: Verify the initial value theorem of f(t) = 1 +e¯t[sint + cos os t]. 3 1 0 2

A: Solution :- As per guidelines I solve only first question .

Q: c) Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y² + 144y + 11yy' −…

A: Given functional is ,                                            I[y(x)]=…

Q: Solve the initial value problem for y as a function of x. (x² + 25) dy %3D 29, у(5) %3D 0 dx

A:

Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

A:

Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

A:

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A: Draw the figure, which is given below. In equilibrium,  mg−kx0=0⇒mg=kx0 Given, mg=4 and x0=1…

Q: A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then…

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A:

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: We have to find the equation of motion for given condition.

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — уз %3 С? (1) (x +…

A:

Q: (t -x)dt – tdx =0; when t = 1, x = 5

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then…

A: .

Q: Find the initial velocity such that the particle will have the same position at t-4s a. and t- Os.…

A: Follow the procedure given.

Q: Use the fourth-order Runge Kutta method to solve for the velocity and position of the free-falling…

A: Given:- t=0 , x=v=0  t=4s

Q: Calculate the third approximation values ​​of the nonlinear equation reading given below with the…

A:

Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

A:

Q: dx 2x - y dt dy

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then…

A: Given that a 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system…

Q: A particle is moving with acceleration a(t)=30t+8a(t)=30t+8. its position at time t=0t=0 is…

A:

Q: A spring with constant k = 2 is suspended in a liquid that offers a damping force numerically equal…

A:

Q: solve the simultaneois equation (dx)/(dt) = 3x + 2y (dy)/(dt) + 5x + 3y = 0

A: Given simultaneous equation, dxdt=3x+2ydydt+5x+3y=0 The eigen value of a matrix is calculated by…

Q: solve the Cauchy problem on the real line for the given initial position and velocity functions and…

A: Given that, and ,  By the Cauchy problem ,

Q: (a) Consider the direction field of the differential equation dy/dx = x(y – 8)2 - 4, but do not use…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: From the given problem, we considered m= 1 kg,  k= 16 N/m, β=10 SO, the mass is released from the…

Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

A: