dP Р(а — ЬР), Р(0) — Ро wherе а,b and Po are constants dt

Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: dy = 2t°y + y + 2t + 1. Show your work and explain thoroughly, when appropriate. dt Determine the…

A: To find the general solution of the given differential equation, first we separate the variables and…

Q: The equation dx/dt = kx is both separable .4 and linear اخترأحد الخيارات

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Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: Find dw whise w - = xy+yz+zz. dt

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Q: dy dt2 dt d'y 8x = 0 - dt?

A: Given that, d2xdt2+dydt=0d2ydt2-8x=0 Now take the derivative for the first equation with respect to…

Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: If r + s2 + y3 = 12, dr/dt = 4, and ds/dt = -3, find dy/dt when r = 3 and s = 1

A: We are given the relation by

Q: dw Find dt if w = xy? + x²z+yz², x = t², y = 2t, and z = 2. %3D t=1

A: In this question we have to find the the differentiation of w with respect to w.

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

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

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what…

A: Given query is to find indicated derivative.

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: In Exercises , find the indicated derivatives.9. ds/dt  if s = t/2t + 1          10. dy/dt  if y = t…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: Use Example 4 to calculate d/dt (r × r), where r(t) = (t,t 2, e t).

A: calculate ddtrxrr where rt=t,t2,et rt=t,t2,et differentiate:-  r't=1,2t,et r x r'=ijktt2et12tet r x…

Q: Suppose you know that dy/dt = 7y and that y(0) = 4. Which of the following answers is closest to…

A: We have to solve the differential equation

Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: dy = ay – b dt

A: In this question, we solve the differential equation by reducing into two-part.

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: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: (2t + 4 dt = J t² +1 antidifferentiation c) Evaluate (Don't forget to include the constant of.

A: Find the integration of (2t+4)/(t2 +1)

Q: t²e*dt dz J2r

A: on solving this we get the

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: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

Q: Find dv if v = t- dt |

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Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

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Q: The function y = 0 is always a solution to a linear homogeneous ODE. True False

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Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: S(t)e¬Jwnt dt_ 2 C =

A: In this question, we find the coefficient for the Fourier complex series cn=2T∫0Ts(t)e-jwntdt

Q: | dy dt e3t +e?

A: We have to find the solution

Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

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Q: a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

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Q: dy Solve the ODE dt = ty(5-y) dy - t y(5– y) dt

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Q: 2t dt J 1+e 1+et

A: By the method of substitution I have solved The integration

Q: Find dv 1 -if v = t dt

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Q: A particle moves along the x-axis so that at any time t ≥ 0 its velocity is given by…

A: Given: v(t)=t2ln(t+2)we know that acceleration of particle is differentiation of velocity of…

Q: Find dw/dt if w = xevz, x = t³, y = 1+ t, z = 1+ 2t

A: We can find the answer as below.

Q: d?x dx + 4 + 5x – 10 = 0, when t = 0,x = 0,x = 0 %D | dt2 dt

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Q: dw Use chain rule to find dt if w = xez, x = t², y = 1- t, z = 1+ 2t.

A: Given w=xeyz, x=t2, y=1−t and z=1+2t We have to find dwdt by using chain rule. Hence, by chain rule…

Q: A suitable substitution to transform the D.E. t dy – y dt = tydt into linear equation will be :

A: Substitution to convert given differential equation into linear

Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

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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