5. dt3 d³x(t) 8 d²x(t) dx(t) - - dt + x(t) = u(t) 14 dt2 d²x(0) 1, dx(0) x(0) = 1 -2, dt2 dt

Q: Suppose that y1(t) and y2(t) have continuous second derivatives defined on the entire real line and…

A: It is given that y1t and y2t have continuous second derivatives defined on the entire real line and…

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

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Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

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Q: |(a) Suppose a particular investor derives utility function - U(x,y) - from owning x units of stocks…

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Show that the partial differential equation has the general solution u(x, y) = e"[fx)+ g(y) where…

A:

Q: 2. Identify the 3rd order nonlinear DE. 3 (dy` A. ( +x³y – xy³ = 0 dx. d³y d²y +y dx2 В. = 0 dx3 d³y…

A: Check each options while it is 3rd order as well as nonlinear differential equation.

Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that  x2 + y2 = 25   .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: The partial differential equation xy Z, 5 Zyy is classified as hyperbolic elliptic none of the above…

A: We have to classify the partial differential equation

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

A:

Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

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

A:

Q: If y=x² - 4x and x = √2r²+1; find dy dt when t = √2.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Write the corresponding differential equation in time domain. F(s) X(s) s³ + 11s² + 12s + 18 s+3…

A:

Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D…

A: solution

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

A:

Q: x-2-x-4 is x-2-x- The differential of y= A dy= -dx x2 B) dy =dx x2 none of the given choices dy=-dx…

A:

Q: 4.1: 1)  Find dx/dt at x=2 if y=5x^2−1and dy/dt=5. dx/dt = ?

A: Given problem:- Find dx/dt at x=2 if y=5x^2−1and dy/dt=5.

Q: (a) Form a partial differential equation by eliminating the arbitrary functions f and g from z =…

A:

Q: (b) Find the general integral of the partial differential equation dz dz. = 7., X- which contains…

A:

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: x-2-x-4 is x-2-x- The differential of y= (A) dy = dx B dy= - -dx © dy=-dx none of the given choices…

A:

Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: In x -dx C. d. 5% dx хе fx(2x +1)* dx е. f. In(x + 1)dx x2 dx Vx + 2 g. x4 h. dx Vx5 + 1 4 i. j. 1…

A: From the given problem:   c).   I=∫lnxxdx..1     Let,   lnx=uddxlnx=dudx1x=dudxdx=du Substitute…

Q: Determine the differential equation of the family of lines passing through (h, k). A. (y- k) dx -…

A:

Q: - Show that the partial differential equation = 0 has the general solution u(x, y) = e"[f(x) + g(y)]…

A:

Q: . y = 2 In(3x² – 1) 2 (In(3x2 – 2)) (3x² – 1) dx dx dx dy = 2. dx 1 6x In(3x² – 1) dy 12x dx Зx2 — 1…

A:

Q: Suppose that one solution y, (x) of the homogeneous second-order linear differential equation y"…

A: This can be evaluated as follows:

Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

A:

Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: dt 4. Solve the initial-value problem dx = -2x – 2y dt dy = -2x + y, dt where the initial condition…

A: To find the solution of the given system of differential equations.

Q: 4. Compute (a) 4 S"(3t2 – 4)z dx - dx 'x (b) x1+t² 4 dt dx -x 1+t2 d

A:

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

A:

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

A:

Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

A:

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

A:

Q: Form a differential equation from y =c(x' +2), here c is arbitrary constant. %3D а. dy (x² + 2) –…

A: y = c(x3 + 2)    ..............................(1) differentiation w. r. to x dydx = c3x2 + 0dydx =…

Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: 3) Find dy/dx Cas %3D X-

A: Given:

Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…

Q: The formation of the partial differential equation by eliminating arbitrary function of z = 3f(x³ –…

A:

Q: ne differential ay of 'uonpuni y = V 5 - x2

A: