dy Consider the differential equation ty-1. ) Explain why you cannot solve this differential equation by separation of variables. b) Shown below is a slope-field for the given differential equation. Sketch the particular solutions that pass through the points (2, -1) and (3,3) c) Find in terms of x and y. Describe the region in the xy-plane in which all solution curves to the differential equation are concave up. d) Let y =f(x) be a particular solution to the differential equation with initial condition f(0) = 1. Does f has a relative min, max, or neither at x= 0? Justify your answer.

Q: 1 (a) Draw a direction field and sketch a few trajectories. (b) Describe how the solutions behave as…

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Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

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: Question: Find Y As A Function Of T If 16y" - 40y' + 25y = 0. Y(0) = 9, Y')O) = 5. Y = . Find y as a…

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Q: Find the equations of the tangent lines to the traces of z=f(x,y)=16−3x^2−5y^2 at (−2,3). What is…

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Q: Consider the slope field shown. (a) For the solution that satisfies y(0)-0, sketch the solution…

A: The solution curve that satisfy the condition y(0) = 0 can be drawn as follows:

Q: Find y" if y = cot(9x 2r+ 8).

A: Given, y= cot(9x4-2x +8)   To find: y''

Q: 1. (a) Find the differential of g(u, v) = u² + uv. (b) Use your answer to part (a) to estimate the…

A: Here we have to find the differentials of g(u,v)=u2+uv .

Q: For the function W= dw = - -8t ³ - 7t, express its differential, dw, as a function of t and at:

A: The function is given byTo determine: The expression of  as a function of  and .Formula Used :

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

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Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: 11. Find the area of the half cylinder S = {(r, 0, z) : r = 3,0 ≤ 0 ≤ π,0 ≤ z ≤ 4} by evaluating a…

A: The half-cylinder is defined as S=r, θ, z: r=3, 0≤θ≤π, 0≤z≤4. We have to find the area of the…

Q: The temperature T in a square region of the (x, y) plane is given by the formula T(x, y) = 2 y – x +…

A: To find- the steepest descent in temperature.  The curve the ant should move is At=xt, yt. This…

Q: 1.) The height above the ground at which a ball is released at an initial height of 122.5m is given…

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Q: 5. We will find the Green Function G(r, r') satisfying I 1(1+1) r2 d²2 G dr.² -G = 8(r — r'), where…

A: 5) Here consider associated homogeneous ODE Noted that its solution is of the form ,then it…

Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00