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

Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: In each exercise, obtain the general solution. 1. dr/dt = -4rt; when t = 0, r = rg. 2. xyy' = 1+ y²;…

A: We solve these differential equations by separation of variables.

Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

A: Given that x2+y2=25, and dxdt=6 we have to find dydt when y>0 and  a) x=0b) x=2c) x=3 Important…

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: dy 4. dz at z = - 4 if y = 3x² – 1 and dt Find dt dz dt

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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

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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: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

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Q: If x^2+y^2=36 and dx/dt=9, find dy/dt when y is positive and (a) x=0: dy/dt= (b) x=2: dy/dt=  (c)…

A: Given: x2+y2=36    -1⇒y2=36-x2⇒y=36-x2   -2dxdt=9   -3

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

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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)…

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Q: Find the solution to dy/dt = 6y Satisfying y(1)=7 y = ?

A: Firstly , separate the variables and then integrate and solve. ∫1ydy = ln(y) +C ∫tn dt =tn+1n+!+C

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: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: if xy+x=12 and dx/dt=-3, then what is dy/dt when x=2 and y=5?

A: Given :xy +x = 12

Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

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

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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: If y = x - 4x and x = V2r + 1, find dy/dt when t = 1= V2.

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Q: Suppose that x = x(t) and y = y(t) are both functions of t. If x2 + y2 = 25, and dx = 2 when x = 3…

A: Given that x=x(t) and y=y(t) are both functions of t . If  x2+y2=25           ..(1) Differentiate…

Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: Find dw/ dt at t = 1 if w = xey + y sin z - cos z, x = 2sqrt(t), y = t - 1 + ln t, and z = pt.

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Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

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

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Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

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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: *show work*

A: Find dy/dt.

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: 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: If x2 + y2 = 100 and dy/dt = 8, find dx/dt when y = 6.

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Q: Assume y′means dy/dt. Solve y′′+ 3y′−7y= 0

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

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Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

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: (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: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: THE IVP

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

Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

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Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

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Q: a) The response of x(t) of a system towards a forcing exponential function is determined by the…

A: Let's find.

Q: Can i get help step by step please

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.