O Given the initicl bouridary conditions y(0) =0, y'c0) = 1, letrmine the, solntiem of %3D Particulsr the frunction of Y= Ae+Be*t2Sinx 2x -

Q: Given that fCx) = x"hc) h'(1)=6 Calculate f'(-1) =

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Q: 11. Use implicit differentiation to determine dx dy given: x*(x + y) = y²(3x – y) %3D

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Q: let X~beta(a,b). find m.g.f ofY=ln| 1-x

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Q: What is the image of the vertical strip  {zϵC:−1<Re(z)<1} under e^z

A: A  conformal map is a one-one and onto analytic map. So, Re(z)=1 to a point. Here f1 is defined by,…

Q: The weight function for y" + y + 3\e*y=0 is none O 10 3e O e II 2 O

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Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

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Q: 7. Draw the dilation of ADEF by a scale factor -with center of dilation at (0, 0). Then, determine…

A: If a triangle is dilated by a scale factor k with the center of dilation at the origin, i.e., (0,0),…

Q: c. y= x*

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

Q: dy/dx and d^2y/dx^2

A: Here; x=e-7t+2 .................. .......(1) y=6e2t+e-3t-4t   ......................(2)

Q: Suppose D is the shaded region in the picture below. Evaluate S y dA 1r=y-y' y= (x+ 1

A: Evaluate  ∫∫Dy dA=?

Q: 1 is 1 H.W Find y' for y = ecosx * tan-1(5x) * (5x² + 1) ?

A: for y , y'=?

Q: Let u: R" x R →→ R caloric. Show the following e" caloric ⇒u constant.

A: Given: u:ℝn×ℝ→ℝ is caloric.   To Show: eu is caloric ⇔ u is constant

Q: y" – y' = 5 – 5e¬*

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Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: Let y = tan dy Then

A: Given data is : y=tan-14x2-1 To find the value of dydx

Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: u2 and ult) ond Ret) ore both diffrentioble %3D functions. Iff uc8) =3 , K(1) = 2, U'I2) =5,…

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Q: u'+ y enx =0 differantial equartion find the %3D pardiculbr general soution. and

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Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: 1. S 5e*dx 2. S(2 – 3e*) dx

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Q: ーy -x+x = 2 +X = o. %3D

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Q: Find Laplace treins form for Ý +4Y+3Y = e y(o) =y co) = 1 %3D %3D

A: Formula Used:L{y''}=s2Y(s)-sy(0)-y'(0)L{y'}=sY(s)-y(0)L{eat}=1s-aL{tneat}=n!(s-a)n+1

Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: Which of the following represents a correct reduction of order for 3y' = 2xy". O Z 3x 2 dz Z 2x = 3x…

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Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: The ops y' =esx-7Y;s Separable

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Q: (20%) Use the following principle of differentiation y' = (y) = (y + Ay)− Y = lim Ay _ dy d = lim dx…

A: Solution is following in explanation step.

Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

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Q: Find S cos(Vx) dx

A: We have to find the value of integration, ∫1xcosxdx It is solved by substitution method, and using…

Q: 3.) dx + e dy = 0

A: The objective is to find the solution of the differential equation.

Q: irst and second derrivative of: 4In(Arctan x)=1-y

A: The derivative of a function f(x) is defined as limh→0f(x+h)-f(x)h. For some standard function the…

Q: classify of the following differentiol equation e^x dy/dx + 3y =x^2y a- both sperable and linear b-…

A: Given: exdydx+3y=x2y To Find: To classify the given differential equation.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.