4. Find the linearization L of the function f(x)=Vx+3 at a = 1 and use it to approximate f(x) = V4.02

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: 1 2) Find the linearization at x = a and use it to approximate f(b). f(x) = a = 6 b = 6.1 V4x+1 f(x)…

A:

Q: 8. Find the orthogonal trajectories of vy = cx

A:

Q: Find general solution for y"+y=0.5cos(t) and state whether it is undamped, underdamped, critically…

A: The second order non-homogeneous  differential equation is y''+y=0.5cos(t) Solution for second order…

Q: 8. Find the orthogonal trajectories of Vy = cx

A:

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A: Make some simplification and rearrange the given differential in exact form.

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Q: Find the linearization of y = at x = 16.

A:

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

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Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

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A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Solve the following initial value problem for u as a function of t: du u = 0 (k and m positive…

A: By first order linear equation  dudt+kmu=0 Here integrating factor is e∫kmdt=ekmt Now we multiply…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

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Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

A:

Q: 1 The linear approximation at = 0 to is V2 – x A + Bx where A is: and where B is:

A:

Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 + 12x2 - 20x + 8.5 using a…

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Q: In x Find the linearization of f(x) = xmª around x = e. Round the gradient and y-intercept, whenever…

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Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 +12x2 - 20x + 8.5 using a…

A:

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

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A: in the given question first off all we have to find the genrel solution of the given differential…

Q: Solve the initial-value problem for a as a function of t. dr 9, x(2) = 0 (2t* – 212 +t – 1) dt

A: We have to solve the initial value problem

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A:

Q: Solve the initial-value problem for a as a function of t. (t2 - 5t + 4) d.x = 1, (t > 4, x(5) = 0)…

A: Givent2−5t+4dxdt=1(t>4,x(5)=0) we have to solve initial value problem t2−5t+4dxdt=1 By separating…

Q: 2: Find the orthogonal trajectories of xy=C.

A:

Q: Is it true that the complementary function xc(t) is a general solution of the associated homogeneous…

A: For a non homogeneous linear system of the form: The general solution is of the form: x(t) = xC(t)…

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Q: 3t – 2 dt t + 1

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Q: (t -x)dt – tdx =0; when t = 1, x = 5

A:

Q: 2. Use substitution to solve the second order y(0)=1 and linear IVP y"-y=0 with y'(0)=0. Hint: Let…

A: Given that, Second order differential equation is, y'' - y = 0…

Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

Q: 1. Use the Chain Rule to find 1. y = u² + 1 dy dx (show your complete solution) . u = x² - 1

A: dydx=4x3-4x

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Q: Solve the Attached problem ?

A: To Determine: solve the following initial value problem for u as a function of t  Given: we have a…

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A:

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Solve the following initial value problem for u as a function of t: du/dt+k/ m u = 0 (k and m…

A: Plug du/dt = u' to make it first-order linear equation.

Q: Solve the initial value problems for x as a functionof t. (t2 - 3t + 2) dx/dt = 1 (t > 2), x(3) =…

A: Solution: Consider the given initial value problem is t2-3t+2dxdt = 1  (t>2) Now, separating the…

Q: Solve the initial-value problem for x as a function of t. (2t³ − 2t² + t − 1) = 0 dx dt = 3, x(2) =

A:

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¬2v.

A: Given information : Family of curves :  x2 = 2y -1 +ce-2y

Q: Solve the initial-value problem for y as a function of z. (64 – ) = 1, y(0) = 2 dy da

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Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

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Q: 9. Find the orthogonal trajectories to the following families of curves: x = ke¯v, where k is a…

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Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y…

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Q: 8. Find the orthogonal trajectories of y cx

A: