d²y dr +24 -52y=0; y(0)=; v'(0)= ; y'(0): dt Use Rod.uction ofE Ordor 3

Q: dz dz Calcula y dy z = x In(y) az = In(y) 1

A: Given : z = x ln( y ) To Find : ∂z∂x, ∂z∂ywe have given four options to determine the correct option…

Q: dy +y = sin (;) cos t, %3D dt2

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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: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

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

A: We will find out the required solution

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

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

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Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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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 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: dx dy + y = x , dt = 3y dt dx dy 1.

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Q: Find dt y = 6t + /9+ 7-t dy dt |3|

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Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: dy -y ze°Cos(E) dt y le) =0 1+らine

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Q: Find the differential dy. 1- 5x y = 4 dy = dx

A: Given that y = (1 - 5x)/4 Find derivative of this y. Here i attached solution of this question.

Q: find dy/dt. y = (esin (t/2))3

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Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: 1 -dt = xy ndif y + J sint+1 secx dx

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: d² y dy } +24% +y=sinh3t – 5 cosh3t ; y(0) = -2, dt² dt y (0) = 5

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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

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Q: Find the differential dy. y = ex/2   dy=

A: Here the given expression is y = ex/2. Apply the chain rule:

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: If y = (t² + 2t + 6) (3t² + 5), dy find dt dy dt ||

A: Given function: y=t2+2t+63t2+5 We have to find dydt

Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: dx T2 +2 and dt dy 2. Find at I = 2 if y = dt dy dt

A: Solve for dy/dt at x=2

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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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: dx dt dy dt x(0) = 2 y(0) = 1 3x – Y 9х — Зу

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Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt

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Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: Can you help me step by step?

A: Given information:

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: y? cos(22) dz da dy Jy/4 by changing the order of integration to dx dy dz.

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Q: Please show all work

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Q: dy/dt=0.3(y-200)

A: Separate the variables and integrate both sides.

Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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Q: dy dt II

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Q: dr Suppose dx dt dy 4, = 3. Find given that r = dt dt x = 8 y = 2 Write your answer in exact form,…

A: Topic = Derivative

Q: Can i get help step by step please

A: Given