dw t- dt dw + x- dx 1, -0 < x < oo, t > 1, w(х, 0) %3D f(x). ||

Q: x2y3-y=x+x2 find dy/dt

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Q: dx + dx dy e; dy = x +y Use elimination to solve: dt dt dt dt

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Q: g(x, Y, z) = /x² +z-2 + sin(xy – x²)

A: Let's find.

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: dy dx ; x = 0, y = 1 , t= 0 dt dt 2) x = t2 + t y = t2 -t -00 <t < 00 %3D fall

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

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

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

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

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: Find the first and second partial derivatives (that is dx' dy? Əx², dy² > and Əxðy of (a) f(x, y) =…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: dx dy - x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

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Q: Find all second partial derivatives of the function f(x, y) = xy + x° + y at the point xo = (2,4). =…

A: Consider the case of a function of two variables, f(x,y) since both of the first order partial…

Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

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Q: dx dy - x – 2y = 16te', 2x - dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

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: find dy&gt;dt.…

A: Given function, y=ecos2pt−1

Q: Q2 Find the second partial derivatives of |(x, y) r cos y +y e*

A: Formula: Second Partial derivitave of f(x,y) fxx, fxy, fyx ,fyy.

Q: 2. Find dy/dx a) y = dt, x> 0

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Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

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Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : df = 32 dx – 4 dy…

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Q: An integrating factor of (x³y² + x)dy + (x²y³ – y)dx = 0 is (a)수 (b) (c) (d)을 2xy 2x

A: Given differential equation is x3y2+xdy+x2y3-ydx=0

Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: dy 3y=e"; y (0) = 1 dt %3D -

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Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

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Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

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Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: d²y – 4y = 0 dy, - (at x = 0) = 4 dx а. dx? y(0) = 2; - d²y b. 5- dx2 sdy dy - (at x = 0) = 0 dx +…

A: To solve the given differential equations.

Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: From an integral equation corresponding to the diffrential equation d'y +x + y = 0 with the initial…

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Q: dx dt dy dt x + 2y -2x – 3y x(0) = 1 y(0) = 2 | |||

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Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

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: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: dx 3D х — 2у dt dy dt 5x — у %3D x(0) = -1, y(0) = 5 x(t) %3D y(t)

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Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: THE IVP

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

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

A:

Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.