Calculate the following antiderivatives: 12t 2t° – 2 dt = +C. (b) u9/4 + 5yū du = +C. dz = +C.

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A: In the given question, the concept of the derivative is applied. Derivative We can use a derivative…

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A: NOTE: Horizontal axis is t-axis  .

Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

Q: Match the D.E. with a direction field: y' = t+ y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2…

A: NOTE: The horizontal axis is t-axis.

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Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: 1. dy dx x + y x

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Q: Given z = 31 sint + 10 and y= 31 cost + 40 da (i) dt %3D dy (ii) dt dy (iii) da

A: Given:- x = 31sin(t) +10 y=31cos(t) +40 To find:- dx/dt  dy/dt dy/dx

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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: Given a = 40 sint + 12 and y = 40 cos t + 29 da (i) dt dy (ii) dt %3D dy (iii) dx ||

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Q: L{t}(s) = / t dt te -at %3D

A: Here we use integration by parts.

Q: If z = x? + y with z > 0, dæ/dt = 4, and dy/dt = 6, find dz/dt when a = 4 and y = 3. dz Answer: dt

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: Find  d/dt [ w(t) ]^2 and show that it equals 2w(t)w'(t)

A: Answer

Q: Find the general solution for y(t) where; dy a. dt + 6t?y = 2t2 dy b. + 10y = 0 dt

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Q: Integrate the following (a )∫eπ31cos (lnt)/t dt   and   (b) ∫2y−11/ y^2−y−6 dy

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Q: a. S ya +1 b+y+cya+1 b. ft² cos 3t dt dy where a 0 and c = 1/(a + 1).

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Q: dy +w?y = 0. dt2 Verify that y(t) = c1 cos wt C2 sin wt is a solution of the DE:

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Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Exercises 4 I. Obtain an integrating factor for the following equations- (x – y²)dx + 2xy dy = o dr…

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Q: Calculate the following antiderivatives: (a) 14t – 3t° – 4 dt = +C. 1. A + 2.5/ū du = (b) +C. u3/4…

A: topic - integration

Q: dT equation dt k(T A).

A: we have been given the differential equation dTdt=k(T-A) this is the first-order linear differential…

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

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Q: | Calculate the following antiderivatives: / 6r – 2° + 7 dt = [T (a) +C. (b) ul/4 1 + 6yū du = +C. 1…

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

Q: Find the general solution for y(t) where; dy а. dt + 6t?y = 2t? dy b. + 10y = 0 dt

A: The given question has been solved in detail

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Q: Find the integrating factor that converts the equation below into an exact equation y de + (2x – y…

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Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

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

A: We can find the answer as below.

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A: The volume of a right circular cylinder is V=πr2h. Consider that neither r not h is constant. Assume…

Q: O1f y= x 4x and x = Vzr?+I, find dy /dt when t r2. %3D

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Q: Find the particular antiderivative that satisfies the following conditions: dx = 5e' – 8; x(0) = 2.…

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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

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A: The given equation is, y=cos4t+11 So, the derivative of the given function is:…

Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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