dx dt ræ(1 – Kı+ay * = ry(1 – K) dt K2+bx

Q: dx 1s+ kıl35-x) +kaly-x) dy %3D dt k, , k. k3 are Con Stants.

A: Given system is dxdt=15+k135-x+k2y-xdydt=k2x-y+k335-y Here, 1k1=5⇒k1=151k2=10⇒k2=1101k3=5⇒k3=15 So,…

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: If  x2 +y2+z2  = 9,dx/dt  =5 , and dy/dt  =4, find dz/dtwhen (x,y,z) =(2, 2,1).

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Q: dt u = xy + y z tzx x = tcost, y = tsint, z=t at t = a 4

A:

Q: d?z dz +3- 2z = te-2t dt z(0) = 0 ; z'(0) = -2 dt2

A: Given differential equation is, 2 z'' + 3z' - 2z = te-2t z(0) = 0; z'(0) = -2

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t² at t=1

A: I have solved the problem with two methods.Final solution is in the box.

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

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

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Q: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

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

A:

Q: dy da at z = – 5 if y = 3x° + 3x and dt = - 1. dt Find - dy dt Submit Question P Type here to search

A: Differentiate wrt  t

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

A:

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dy Q1) Compute for y(x) = sec (2x) + 2x-1 and dt x(t) = 4cos(t2) at t-1 %3D

A: From the given problem:   yx=sec32x+2x-1xt=4cost2   Now applying the chain rule:   dydt=dydx.dxdt…

Q: 6. dy dx + y?x = sin y, dx ay = 7. dt dt 8. Σa (x) dx) d0y = f(x), where d°y = y, dx°

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Q: the = x + y + 3z dt dy a) = 2y + 3z dt dz = 3z %3D dt 1. Write the linear s Find the eige envalı

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Q: Using d²y(t) dy(t) + t dt + 2y(t) = 0, and y(0) = 0 and y' (0) = 1. t dt?

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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: dx dx Find - - for x = x(t) defined implicitly by V +V x In(t) = eVxt. Also dt evaluate at %3D dt…

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Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

A: Given query is to find derivative is nge chain rule.

Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

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Q: Find dy/dt if y is as follows. t2 + 4 y = In 7 - t dy dt II

A: We use logarithmic properties to simplify the given function and use chain rule to solve this…

Q: dy for 2xy - 2x + 3y3 = - 42, with the conditions dt dx 3 - 12, х%3D3, у%3 Assume x and y are…

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: dy Find dt y = (21+ et) In t dy %D dt (Type an exact answer.)

A: To find the derivative of following function

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

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Q: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: Can i get help step by step please

A: To find dx/dt when y = 2 and dy/dt = 5

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: 4) Let T=xy ln (x2+y=]; X=e'cosu Cosu, y= e sin u. Find dT, at lu,ul= ( "B,0) at (u,u)= ( "/½ ,0)

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Q: Can you help me step by step?

A: The given function is

Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

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Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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Q: Please show all work

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Q: If+y = 25 and dz/dt = 5 , find dy/dt when y is positive and %3D %3D (a) z = 0 dy/dt = 0 (b) z=1…

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Q: Can i get help step by step please

A: Given