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Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: What is 'z' in the given Bernoulli DE (6xy³ – y)dx + 2x?dy = 0? Select the correct response: y2 -y?

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Q: By algebraic substitution, the integral - dx dx is converted to: 4+x 2ydy (A y+4

A: Option a is the correction and other option does not satisfy the given conditions

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

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Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

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Q: Given z = 15 In(t) and y = 225 t then find %3D dy dx d'y dr2

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Q: The DE: dY - 4xy +5y² xy + 3x? can be transformed into a seperable DE dx in x and z by using the…

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Q: That is *z' in the given Bernoulli DE (6xy³ - y)dx + 2x²dy = 0? lect the correct response: O -y-2 y2…

A: Rewriting it, dydx=-(6xy3-y)2x2dydx=-3y3x+y2x2thus we have,dydx-y2x2=-3xy3

Q: 4хy + 5y? xy +3x? in x and z by using the substitution y = xz dy = can be transformed into a…

A: We will use the substitution to try to transform the given differential equation into separable…

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: Given the non exact DE y(8x-9y)dx+2x(x- 3v)dv=0. find f(x).

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Q: Use appropriate substitution to solve the following (iv) zy" + (y/) 0. %3D

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Q: E valauate the JJ x +2xy +ydy dx when step size of x-0.2 and step size of use the Trapazaidal Rale…

A: given I=∫01∫02x2+2xy+y2dydx with  h=0.2 let x0=0.2 , y0=0.5 let fx,y=x2+2xy+y2 substituting the…

Q: Given y = Vx³ + 1, evaluate dy using delta process. dx

A: Given y=x3+1evaluate dydx using delta processSolution fx=x3+1 dydx=fx+dx-fxdx  dydx=x+dx3+1-x3+1dx…

Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: For the given DE with coefficients linear in two variables, do the following: (6x – 3y + 2)dx – (2x…

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: of Find and dy f(x.y) = /2x + 3y? df (Type an exact answer, using radicals as needed.) dx II

A: We can solve this as follows:

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

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Q: Find for the following by using appropriate rules: dx i. y = Vt , x: X = t+1

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Is this 2-form exact? w = x dx A dy

A: Given that ω=xdx∧dy To check this  2-form is  exact or not.

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: By algebraic substitution, the integral - dx dx is converted to: 4+Vx 2 dy A y+4 2ydy B У+4 ydy (C)…

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Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

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Q: Given the DE. 3dy + ydx = (1-2x)y4, Rewrite the DE into Linear Form at v O dx-v = 2x+1 dx-v=2x-1…

A: Given: The differential equation 3dy+ydx=1-2xy4dx Rewrite the given differential equation in linear…

Q: Exercise: Answer the following by finding dy/dx. 5sin-lr cosh x (a) y = Vsect x + In 7 4 (b) + In y…

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Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy (Write as an exact decimal.) %D

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Q: 4 i /," x’dx using four subintervals. Calculate the trapezoid approximation of O T5 = 61.24 O T5 =…

A: Dear user, You need to find step height and using this you need to find endpoints of interval. Then…

Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…