Use the laplace trans form to selve y- Hy'+ 4y=1 it Octci and o if +>\, yro)=0, y'lo) = I. (a) ylH)=t-e2# +ste*- (+-1) - ' 2 (t-1) %3D (b) 2(t-1) + +2 (+ -1) + 3e 2+ (c) y(t) - że't je + +. (o) yH)=e*(G,•C;+) +|-u(t-1) (e) None of these.

Q: Differentiate 2 Y = t² + 5÷t² - 4t² + 3 Y' = ?

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Q: graph of (x) = x' - 2 is shown in the figure. Find 6 such that if0 2 ]x - 4] 2 8, then IAX) - A. ô =…

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Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

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Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

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Q: Calculade the Pomer Seriee af na o y'=

A: The given differential equation is 2-xy''+xy'+y=0. Let y=∑n=0∞anxn. Then, y'=∑n=1∞nanxn-1…

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: (D² - 4D + 5)y = e¯*; yp a. Yp 10 b. y, =#e* 10 C. y, =e* 10 d. y, =e* 10

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Q: Find dy/dx: y = In [(1 + t^2)/(1 - t^2)]

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Q: +o0 - Find Ul-1/i, 1/i]- i=1

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Q: Find dxdz -2 -3lnax) a= constant

A: find d2ydxdz y=(z14-3lnax2)-2

Q: Fnd llull, lv , Uov, and d (4,v). (-1,7) , v- (1,9)

A: According to our company guidelines we are supposed to answer only first 3 sub parts. So here I'm…

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

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Q: Find r'(t), r"(t), r'(t) •r"(t), and r'(t) x r'"(t). r(t) %=D 흑래- 26j + 하하k (a) r'(t) (b) r"(t) (c)…

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Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

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

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

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Q: Find all residues of the function z (2-2) not including the residue at infinity. "

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Q: Show that 1 1 2 y? 2 = (y? – *)(2² – a²)(2² – y') 4,

A: We have to prove that  We will it by using the properties of determinants.

Q: sinh x 20. 1x1-3 A) 2. B)-2. D) 0.

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Q: (b) 를/ dx 3

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Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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Q: t seel dx

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Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 클레 - 3tj + (a) r'(t) (b) r"(t) (c)…

A: We need to find derivative and dot and cross products.

Q: Solue coscx+y) + (るご+zy+coscx th)), dx

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Q: y'= (6x-2y-3)10 When 9polyg the vavable change u= - 6x-2y-3 the eqn converts 'into? Oa du = (-2u" +…

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Q: fin y" given that x^2 - xy + y^2 =3

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Q: Find the complex remainder of the function: f(z)= 2z^4(3z+5)e^(3/z^3) Remember that: e ^ u = 1+ 1/1!…

A: We know that the residue of a complex function is also known as the remainder of the function. We…

Q: Series Solution Method. In each of Problems 1 through 20, solve the given differential

A: Given,         y''+xy=0;        x0=0

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.