Solve the following DE t''-3t'+2t=3-4x; t(0)=1/4 , t'(0)=3

Q: Draw a slope field for the differential equation / = 0.2x² + y

A: We have to draw the slope field for the following differential equation, y'=0.2x2+y

Q: Show that the following differential equations are homogenous and solve

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Q: Select the differential equation that matches the given slope field. Is 1 141 O=-(2+1)*y? o -- 0--点

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Q: What is the differential equation of the orthogonal trajectories of the family of curves x-3xy- 2y²…

A: This is a simple question based on differential equations which could be solved using the basic…

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: Write down a differential equation of the form dt all other solutions diverge from y = 4 as t →∞.…

A: Let us consider a differential equation dydt=ay+b  such that the solution diverges as t→∞, y=C The…

Q: Which of the following is the differential equation of the family of Straight lines with slope and x…

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Q: Determine the form of a particular solution (without computing the coefficients) to the differential…

A: The given differential equation is y''-14y'+49y=3te7t

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: dN + N = Ntet+2 dt

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Q: Find the 4th order differential of the function y=√2x+1.

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Q: What differential equation corresponds to an RC circuit with a resistor of R = 100 and a capacitor…

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Q: Find the general solution of the differential equation with the help of lablace transform

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Q: D. Solve the differential equation using Loaplace transform of y" + y = 6sin 2t ; when y(0) = 3 and…

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Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

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: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

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Q: The number of customers in a store is modeled by the function P that satisfies the logistical…

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Q: Solve the given differential equation by undermined coefficients ya) – 5y" + 4y = 2 cosh x – 6.

A: By Bartleby policy I have to solve only first one as these are unrelated & lengthy…

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

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Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

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Q: y(4) 4х + 2хе %3D

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Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: solve for the differential eq   (8x−10xy+4y^2sin^2 (x) )dx=(2ysin2x+5x^2−4xy)dy

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Q: y = Ax² + Be*

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Find the differential equation which has y= asinx+bcosx+xcosx

A: Given: y=asinx+bcosx+xcosx                                   ..1 for finding differential equation…

Q: Find a differential equation whose general solution is y = ciet + cze-4t. %3D

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Q: Obtain the differential equation of the family of lines passing through (-1.1).

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Q: Find the differential equation having as solution of y = x sin(xtc) .

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Q: If y = sin2x, the derivative dy/dx is equal to a. cos2x  b. sin2x c, 2cosx  d. 2sinx (SOLVE BY…

A: Solving the equation by the method of differentiation.

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: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: V34

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Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

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

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

Q: Solve the differential eguation 3-

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Q: Find the differential equations having as solution of y = x sin(xtc) .

A: We find the differential equations having as solution of y = x sin(xtc) .

Q: 2) Obtain the differential equation of parabolas with vitex and focus on the x-axis

A: To find: the differential equation of parabolas on the x- axis.

Q: A man is walking at a rate of 1.5 m/s toward a street light which is 5 m above the level ground. At…

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Q: Obtain the Differential Equation of all circles passing through the origin and (0,8).

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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: find the differential equation of a family of parabolas with an axis parallel to the x-axis

A: We have to choose the correct answer from the given option according to the given condition