Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sx(t) = 11 – t ly(t) = 17 – 4t %3D

Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t3/2 at t = 1. Also…

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Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

Q: t^2 y^′′+aty^′+by=0, t>0 Define what type of equation is  mentioned above ?

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Q: (c) Find dy/dx at t = T/3. (d) Include in sketch for (a) the tangent line to the curve at t = T/3…

A: We have to find the equation of tangent line.

Q: A) The position of a particle P(x,y) at time t is given by: x= (2t +3) , y =+t.Find the distance it…

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Q: The position of a particle in the xy-plane at time t is r(t) = (t+2) i+ (t- + 3) j Find an equation…

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Q: + (4xy – 3x²) dy = 0, find an integrating factor of the form d equation. %3D

A: First we have to find integrating factor for given differential equation and with the help of…

Q: Show that the equation is homogeneous and find its solution. dy/dx=x+y/x

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Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

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Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: 1. dy dx x + y x

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Q: olve the equation x y² dy = (5 x³ + y³) dx using Homogeneous method.

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Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: Find dy dx2 Q2 when t = 1 if given the parametric functions as below, x = 3e5t y = te-5t

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Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: Find all solutions of the equation: dy​/dt=yt−y−t+1. Stationary and non stationary

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Q: |e*y dx+e* dy; C: r(t) = (t+ 1, ),-1si<3 Exercise 97.

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Q: 1² + y² dz dy dx – (Evaluate by changing to either cylindrical or spher- ical coordinates.)

A: Here we will evaluate the required integral.

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

Q: dx 6 when x=1, what is dt dy If y=x is expressed with parametric equations such that dt

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Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

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Q: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: dx dy. If y =x is expressed with parametric equations such that - 6when x=1, what is dt dt 12 -6 -12

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: dy х у ++1 y dx

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Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…

A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3   Apply the chain…

Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

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Q: (2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

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Q: 2. 2y dx - x dy = 0

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Q: Can you help me step by step with this problem?

A: Firstly, we set u=2t and v=(3t^2-70)^5, then we fid du/dt and dv/dt

Q: 6. dx 4x + 3y 2x+y

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Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: Find the integrating factor that converts the equation below into an exact equation y de + (2x – y…

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Q: Find dy/dx. - tsin(t), y = t² + 5t %3D %3D

A: givenx=tsinty=t2+5tfirst we differentiate these two then we evaluate dydtdxdt which is equal to dydx

Q: roțațion 90° counterclockwise about the origin Ay R T

A: The figure SRT is to be rotated counter-clockwise about origin by 90°. The resulting figure will be…

Q: Solve the DE shown below, with boundary condition y(1) = 1. (1 Point) %3D xdy - (4y + x')dx 0

A: GIVEN EQUATION IS LINEAR DIFFERENTIAL EQUATION.

Q: 3. dy dx x² + xy + y² x²

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Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

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Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

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Q: dy + y dx dy – 3xy = 5y sin x xy dx2

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