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: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: Find: a) The PDF fy(y) b) The PDF fw (w) W = { Y 16 Y≤ 16 Y > 16

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Q: The weight function for y"- y +3de* y = 0 is 3e* none O ex

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Q: y' = y = eP(p + p√p)

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Q: B)Is w = Ze² analytical function or not?

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Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

A: on diffrentiating with respect to x we get

Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: Consider the DE y"+exy'+ (sinx) y = ex+2lny then the order of the DE is ✓ and it is

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Q: 2 y = √√√x² + 1

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Q: Suppose thet the filowing Aransforuution Conneclss the (x') and (ti) codmate ک ماول se4ス?) e え(スーx)…

A: Handwriting solution given.

Q: y" – y' = 5 – 5e¬*

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Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: ow the processs on separating the variables of the given DE ich that all terms containing x must be…

A: Remark: A first-order differential equation is said to be separable if dy/dx = f(x, y) , the…

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: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

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Q: ーy -x+x = 2 +X = o. %3D

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Q: Given f(x, y) = 4x³y², evaluate f(1,y) and fy(x,2).

A: We are given a function: f(x,y) = 4 x3y2 We need to find the partial derivative of the given…

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: If u = 2-x, x/2-xd

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Q: Find the solotion of the differential eaoation thot satisties the qiven nital condiion

A: The given differential equation is,

Q: dx dx A lim 25 - x2 c+5-°o 25- x² dx dx B lim c+1+°c In(x²) 4dx 4dx o Vx(x+6)¯ c-o /x(x+6) lim . E…

A: follow next step

Q: Given that f(x, y)= 2x* +3x'y+6xy'-y. Find: i. f ii. f, iii. fx XX iv. fy v. Show that xy = f

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Q: An integrating factor for y'+8z°y = sin z is given by (a) 2z (b) In(z*) (c) z4 (d) 5e2z

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Q: 1- Sº, S², x² e*y dxdy exy dxdy 2 -1 1

A: We have to evaluate ∫-10∫-1yx2exydxdy

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: f (x,y) =x³ cos y Given df (2, 1) дх of and (2, л). Evaluate ду

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Q: W.Find A' for the given cholce of U. 1A (3,6, 9) U (x/0<x$ 10 A 2. A = (1, 2, 3) U = (0, 1, 2, 3, 4,…

A: From the given information we find the A compliment .

Q: Let H (2) places. = Z In(z) Compute H'(2.2). Round your answer to 2 decimal

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Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: If y = Vln(x)+ In(/E), then y' Select one: 1 O a. (z)u1^z O b. (z)u1^z O c. 2z /In(z) Od. 2z /In(z)…

A: Differentiation

Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…

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

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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.