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A: We have to factor 54-3x-x^254-3x-x^2=(6-x)(9+x)

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: %3D x2+7 X2 +7 to flx1-メ= LtzX as xI oc ニ I + 7/x?

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Q: al equation - y² , y(1) = 2 is hod with step siz nd off to 2 place

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Q: -2xy 3) y' = iy = -5 when x = 2 Ans: exact; x²y + y = -25

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Q: 2 13 y+y+y%3Dx"+4X+12%

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Q: Q4/ B/ If Ø = (x³y²z) and A = 2xz i - 3y²j+ 3xy²k Find 0(ФА) ay əx the point (2, -1, 3)? at

A: Given: ∅=x3y2z and A→=2xzi→-3y2j→+3xy2k→  To find: ∂∅A∂y∂xat the point 2, -1, 3 To solve the problem…

Q: Q₁ /Find x, y E R for: -i+1 2-i c) √

A: To find x, and y for the below complex number. −i+12−i

Q: (2) y" (t) - cy'(t) + gy(t) = 6t²²t where: you) = Y(u) =

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Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: 5. (D³2D+4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: [-2 + j3 -1/3 6235°. -j d) D =

A: Given -2+3j-1/3-j6∠35First we will convert 6∠35 to rectangular formWe know that x=acosθ and y=asinθ

Q: "+y=と(t - kT), y(0) = 0, / (0) = 1. k=1

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Q: у' -у - 2у3 36(t -2)+ e%; у(0)-D0, у(0)-3 y(t) = D %3D

A: NOTE: Refresh your page if you can't see any equations. . take Laplace

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

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Q: n(Σxy) - (Σχ)(Σy) VnEx - (Σ] [ nEy? - (Ey}]

A: Given Data is Baby x y A 8 56 B 5 44 C 11 79 D 13 72 E 10 70 F 5 54 G 18 94 H 15…

Q: = (2)ng ? i=177h! ;=(77X 2=4 [27³] -2t [i]e [1] x [ + =] X + - S. = (0)x Z- 0 2 y = X

A: As per the question we are given the State-Space representation of a dynamic system and we have to…

Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

A: To find the solution of the given differential equation .

Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: Q.2 JJR ex2-2 dxdy, where R between x2 =-y, y = 0 and x = -3 , y = -9

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Q: y(t)+5 y(t)+4y(t) = 2e" -21 %3D

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Q: Q1) L-1 s(s a) cosht -1 b) 1-cosht c) (cosh2t - 1) d) (1 - cosh2t)

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: x3y5 Q3: Let x = 2 ± 0.005 ,y = 10 ± 0.01,z = 20 + 0.01 find u = %3D And fined the error ?

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Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: 23- y" - 2y + y = 0; y₁(t) = et, y₂(t) = tet

A: 23. Given y''-2y'+y=0   Also given y1t= et,  y2t=t et   To verify: the functions y1, y2 are…

Q: 3. D'y - D'y- Dy + y = 0 (AD4

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Q: 1. (D 2 + 3D + 2)y = 4t 2 By: (a) reduction of order, and (b) variation of parameters.

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Q: F(s)= 2s+8s+12 f(t)=?

A: according to the question we need to find the inverse Laplace

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

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Q: u? – 1 du J2x u² + 1 3x - 56. g(x) :

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Q: I Y=t5メPYove th y-2(21くるど

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Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

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Q: for the -j 3 O de terminant 2-j3 3 2 i-s 1

A: det3j2-3j3-3j-120-j1-j=3jdet-12-j1-j-2-3jdet-3j201-j+3·det-3j-10-j=3j-1+3j-2-3j-3-3j+3-3=-3-6j

Q: Q.2 R ex2-2 dxdy, where R between x = -y, y = 0 and x = -! -3, y = -9

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Q: dy Given y = 2u? and u = 8x – 1, then dx - 8(64x? – 2x + 1) 0 خيار 4 48(8x – 1)2 0 خيار 3

A: The derivative of xn is calculated using the formula, ddx(xn)=nxn-1 .

Q: (2t – 4 Ost<2 (D? – 1)y = 2 t22 у(0)-0, y'(0)-1 Find L{y}

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Q: Ex3) show That y= ē" is Solution Lor y+y`-2y=o

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Q: -1st251 t一3 0. Sketch ) xの b) x(t)

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Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: -)-= 0 ,y'at y = a (b is constant)

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Q: 5. (D² + 1)y = 10e2x; when x = 0, y = 0,y' = 0 %3D

A: Find complementary function and particular integral then solution is given by y(x)= CF + PI .

Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: 2. Given y = 25e-2x verify that y' + 4xy = 0 Your answer

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Q: et2-2 2.2 R dxdy, where R between x2 = -y, y = 0 and x = -3 , y = -9 %3D

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.