(B) [11]13'[xlí3= [7]13 : (HINT: first try to bring the equation to the form [x]j3 = [a]13 ).

Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

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Q: 2. Eliminate the arbitrary constants: x²y = 1 + Cx 1 Add File 3. Obtain the differential eguation of…

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Q: superposition

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Q: 3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.

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Q: Find the differential dy of the given function.     y = 3x2/3

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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: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

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Q: he Bernoulli equation for y by making 4y + y³. - following initial condition: u(0)

A: Introduction: A differential equation is a mathematical expression that contains the derivative of…

Q: Find the differential equations for each family of curves under the following conditions: c)…

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Q: in the following problems, obtain the differential equations of the given families of curve whose…

A: 1) The equation of the circle will be of the form The differential equation in this case will be

Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

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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: 5. Find the differential equa tion of (x-c.)" †C2Y C3

A: We will eliminate the arbitrary constants. As there are 3 constants so it'll be differentiated…

Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

Q: 4. Find the positive root of the equation correct to 3 decimal places, using Newton-Raphson method…

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Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

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Q: Find the Wronkian (up to a constant in front) of any two solution x1(t) and x2(t) of the…

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Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: Solve the given differential equation using indeterminate coefficients y''' - 6y'' = 3 - cosx

A: The given differential equation is y'''-6y''=3-cosx. Its auxiliary equation is m3-6m2=0. Solve it as…

Q: Q2// FIND THE GENERAL SOLUTION WHEN THE DIFFERENTIAL EQUAION IS ỳ + 3ỳ + 2y = 36xe* %3D

A: Given the equation y''+3y'+2y=36xex Which is in the form of y''+py'+qy=s so, p=3, q=2 and s=36xex It…

Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: of the differential equati

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Q: at

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Q: 3. Plot the slope field for the differential equation = y² – x and sketch the solution for the…

A: Given: A differential equation dydx=y2-x. To sketch: Slope field of given differential equation and…

Q: 15. Use differentials to approximate V26.

A: To approximate263

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

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Q: the differential equati on 21?y -dy-34=5€ dx Solve

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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

A: Giveny=4x-53   ...(1)

Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: Find the differential of y² + x = 4.

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

Q: 4.3√√√7

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Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

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: Show that y1 = 1 is a solution to the first order Riccati differential cquation given below, and…

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Q: 1. Consider e* – 2/x – 3 = 0, using Secant Method with initial points xo = 1 and x, = 2, calculate…

A: The given function is: ex-2x-3=0Initial points are:x0=1x1=2

Q: What are the roots of the characteristic polynomial for the differential equation y" + 4y' – 5y = 0?

A: Given differential equation:-   y" + 4y' -5y = 0

Q: Compute the approximate value using differentials. /272 √234 The final answer should be in fractions…

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Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Find a particular solution to yp of the given equation. In all of the problems, primes denote…

A: In this question, concept of Variation of Parameters in Differential Equation is used. A…

Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

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Q: *-({ 3*+(tans

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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: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

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Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: Parabolas with vertex on the y-axis, with axis parallel to the x-axis, and with distance from the…

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: (1/4) Estimate the value of 82 a. approximation b. differentials

A: To estimate the value of 8214 by using a approximationb differentials

Q: The first approximation P of the solution to the equation f(z) = x² – 8 that is near to Po = 4 using…

A: As we know that the iteration formula of Newton's method is:   Pi+1=Pi-fPif'Pi  i=0,1,2,3.....…

Q: 3 Q2. Find an approximation to V11 using 4 steps Newton's method.

A: