Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm + CxP + Dx where - %3D A is

Q: Let y = V7 – x. %3D Find the differential dy when a = 4 and dx 0.3 Find the differential dy when x =…

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Q: Find the goveming equation and associated boundary conditions by minimizing the functional, I.…

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Q: Let y = 5a2. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4…

A: ∆y = 5(x + ∆x)^2 - 5x^2= 5(x^2 + 2x∆x + ∆x^2) - 5x^2= 5(2x∆x + ∆x^2)= 10x∆x + 5∆x^2 So when x = 4…

Q: Let y=x2+2x. Compute Δy and dy at x=3 if dx=0.2. What is the difference between Δy and dy? That is,…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = V4 - x2 dy =

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Q: Q1-lf x= cot-VE, y= , find dy dx' dx2 at t = 2. t+1

A: We have to find first order and second order derivative of the given parametric functions.

Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential…

A: Topic = Derivative

Q: So SAF+1° y¹/3 x7 +1 (Hint: Change the order of integration to dy dx.) Y dx dy.

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Q: Find the particular antiderivative that satisfies the following conditions:…

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Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Find the particular antiderivative that satisfies the following conditions: dx/dt=8e^t−7;…

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Q: 1. Find the antiderivative a) S(eš* – ) dx b) Se-4*dx c) S Vx(2 + x²) dx d) S-2xe10 - x² dx e) S…

A: (a) Given that,

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: dy – 5x-2+ 2x-1 – 6; y(1) =7. dx |

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Q: dy y у-х Reducible to =2 + cos dx Y(2) = 2 I| Homogenous method

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: dy=(0.5x- 3) Co 3)° dx

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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: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: In the given DE, cos z + In y + ( +e) dy 0, de integrating M (x, y) with respect to x generates a…

A: Here we are given a differential equation And we have to find the function g(y). For this first we…

Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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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: Let y 52?. Find the change in y, Ay when r = 5 and Ar 0.1 Find the differential dy when x 5 and dx =…

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Q: Construct the Green's function for d²y dx² dy + (k?x² – 1)y = 0, + x dx subject to the boundary…

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Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: If y=f(x) satisfies the given DE and prescribed initial condition, then y(e?) = dy 1 ; y(1) = 0 dx

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Q: Let z(x, y) 2x2 – 3y? where a 2s – 4t & y = 9s + 8t. he at dy dx az Calculate ds dz by first finding…

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Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

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Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: In solving the antiderivative of f(x)= 3sin(x) + 4cos(x) +5 by miscellaneous substitution, the…

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Q: Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

A: We need to find dz.

Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

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

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Q: Let y = 3a?. Find the change in y, Ay when x = 1 and Ax = 0.3 Find the differential dy when x = 1…

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