g'(a Suppose 8 (x) = Vx. What is the correct expression for the result of g "(= A 3x В 2x 2x - 3 3x

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: Find the general solution for the equation below by using vaiation of parameters method. y"+y=1/x…

A: We have to find the general solution of the differential equation by using a variation of parameter…

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: 3. Determine a homogeneous linear equation with real, constant coefficients that is satisfied by: y…

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Q: 1. Differentiate the implicit equation with respect to x. x³ + y³ ln(x) + e²y = 4

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Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

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Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4

A: dxdt(3t4+4t2+1)=23=>dx=23dt3t4+4t2+1=>dx=23dt(t2+1)(3t2+1)=>dx=23…

Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: at

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Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: y(4) + 8y″ + 16y = 0

A: Given, y4+8y''+16y=0

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

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Q: The general antiderivative determined by - x² - 3x +2 is dx

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Q: How do I find the general solution of y''- 2y'= e^x * sinx using the method of variation of…

A: y''-2y'=ex sin x Auxiliary Equation: m2-2m=0⇒m1=0, m2=2 Complementary function  :  y=c1+c2e2xthis…

Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

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Q: The integrating factor of the non exact DE ydx-xdy=- is -1/x^2, show your solution

A: We have to find

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: R(x) = F/2 π dx

A: We have to evaluate the integral: R→x=∫0π/2sin2x3x+1, lnx2-1,xx2+1dx   .....(1)

Q: Solve the initial value problem given by y' = (x − y)2 ,  y(0) = 0 What is the interval of…

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Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: The integrating factor of Y + 3y cscx= cotx is?

A: Consider the given differential equation, y'+3ycscx=cotx This is the first order linear differential…

Q: Use variation of parameters to find the general solution of the differential x²y" - 5xy' + 5y = 4x…

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Q: How do I solve dx/dt+2x=3 with a particular solution of xp=3/2?

A: To find the general solution of the equation, given the particular solution

Q: Solve the differnetial equation: dy/dx=3/x^2-3x^2+2 with the initial conditions (1,8). show work

A: By using variable separable method we can calculate the given differential equation. See attached…

Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: First Solve differential equations ,

Q: Solve the initial value problem by using integration. g' (x) = , 9 (1) = 4 x+1 %3D

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Q: According to the Ideal Gas Law, the pressure P, temperature T, and volume V of a confined gas are…

A: We have to use differentials to approximate the percentage change in pressure if the temperature of…

Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

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Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: Jesaki Inc will sellN units of product after spending $a thousand in advertising, as given by N = 73…

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Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: 3. Find the general solution of y"-3y'+2y=e2* cos x [using variation of parameters]

A: See solution below

Q: -Find for: y= sinV1-t dx

A: We have to find dydx for y=sin-11-x4.

Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

Q: find the general solution of the differentialequation and check the result by differentiation.dy/ dt…

A: The given differential equation: dydt=x32 Integrate both sides of the differential equation with…

Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…

Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.