Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use technology to obtain It Describe the slopes of the lineal elements on the lines-0y-7, y, and

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the…

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the…

Q: dy y = x-'(a² + x²)¿, solve for dx

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: 1+vx [8] Find y" of y =

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Q: A model for the velocity v at time t of a certain object falling under the influence of gravity in a…

A: From the solution draw the graph on the direction field.

Q: (D² +1)y = sec x. %3D

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Q: Let xy = 2y + x. If you implicitly differentiate this dy equation, and then solve for you dx (a-y)…

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Q: Differentiate the function. y = (3x* - x+ 1) (-x³ +9) %3D y' =] %3D

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Q: y' = (x - 1)(y-2), y(2) = 4

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Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: 12. y = 3t 1+t³ X= 3t² 1+t³

A: We can find y' using chain rule as below.

Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: yy"-1 y'

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Q: Find the general solution of the equation by the variation of parameters method: y" – 2y'+ y = æ 2e"

A: We use the procedure of method of variation of parameters.

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

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Q: (D²-3D-2)y = 0 Find y when x = In 2 when x=0, y'= 9, Y=0, y=0 4.

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Q: A particle is moving with the given data. Find the position of the particle. a(t)= t^2 -5t + 4,…

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Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: If xy + 3e = 3e, find the value of y" at the point where x = 0. y" =

A: To find the y" for  xy+3ey=3e at x=0

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

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Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: (a) A particle is moving in the vertical plane and the height of the particle is given by…

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Q: what is the yp(t) for the equation?

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Q: Find y as a function of tif y(3) = 8, y'(3) — 9. Y - 49y"+126y + 85y = 0,

A: Find  as a function of  if  ,  .

Q: (2y² + 3x) dx + 2xydy = 0 Determine an appropriate integrating factor (x) or (y) that transforms the…

A: Solution :