Find the position function of a particle moving along a coordinate line that satisfies the given conditions. a(t) = 3sint-cost, s(0)= 4, v(0) = 0

Q: Use the table to find the instantaneous velocity of y at the specified value of x. O A. 1.5 ОВ. 1…

A: To find the instantaneous velocity of y at the specified value of x

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: A) The position of a particle P(x,y) at time t is given by: x= (2t +3) , y =+t.Find the distance it…

A:

Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dy + 2t2 - 6y = 0 dt dt? The…

A:

Q: 4) The position function of a particle is given by F(t) = (t², 5t, tť² – 2t). When is the speed a…

A:

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

A:

Q: 1. dy dx x + y x

A:

Q: The output at a certain factory is Q(x, y) = 6x² + 3e36. ỹ+ 3y. %3D where x and y denote,…

A: The function is Qx, y=6x2+3ex36y+3y2. The marginal rate of substitution is given by dydx=-QxQy…

Q: Find the general solution for y(t) where, dy 10t dt y II

A:

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

A:

Q: At what time t does the speed of a particle moving in 3-space with position function r(t) = ti+tj+…

A: To find the time at which the speed of the partial is minimum. Note that, the velocity is the time…

Q: b- Yt dt + dBt dY; 1-t

A:

Q: verify the given linear approximation at a=0 . Then determine the values of x for which the linear…

A:

Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

A:

Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: what is the dependent variable and linearity of the DE: d(xy)/dx + xy=0?

A: We will find out the required values.

Q: Find the linear approximation to R(t) = Vt: %3D at t=32. Use the linear approximation to approximate…

A:

Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

A:

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

A:

Q: Use the technique of variation of parameters to find a particular solution to the DE y" – 2y + y =…

A:

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: Since y"|? v0 at x = -1/2 e we have a relative minimum at the point (c, f(c)). Substitute c = 5e¬1/2…

A: Solve it

Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: d2y/dt2+5(dy/dt)+6y = t2+2t  Solve the equation using the method of change of parameters.

A:

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

A:

Q: B. Determine the general solution of the following nonhomogeneous linear equations using the method…

A:

Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Find the general solution of d²y x(x +2) dy + (x + 2)y(x) = x³, dx dx? given that y, (x) = x and…

A: The given differential equation is solving through the variation of parameters below.

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

A:

Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

A:

Q: Consider that the heat flow is described by the equation Pu + xe2t ди %3D with BC: du(0.t) Ou(3.1)…

A:

Q: Use the Improved Euler Method to estimate the values of the function y, solution of the imutial…

A:

Q: Find the Green's function for the Helmholtz equation (V2+k²)u = 0 in the interior of the unit square…

A: Given the equation                       ∇2+k2u=0, in the interior of the unit square 0≤x, y≤1, with…

Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

A:

Q: d²y +y = d' sec{t) dt dt² dy y(0) = 0; (0) = 1 dt

A: The given differential equation is,d2ydt2-2dydt+y=etsec(t)

Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

A:

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

A:

Q: xe' dx + x² ydy 3. ; Compute along the curve x = 3t, y = t ,0St<1 С:

A:

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: e f(x, y) = x² + y²;x = t²,y = 2t, find dz with t = 2 dt

A:

Q: 3. dy dx x² + xy + y² x²

A:

Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: xe" dx+x²ydy Compute e'dr+r'ydy along the curve C: * = 31, y =t² ,0<ISI

A: Topic: application of integration

Q: 4. Find the general solution of the equation t’y" -t(t +2)y'+(t+2)y = 2r° using the method of…

A:

Q: 1. dy x + y dx X

A: Solution :-