J 2x – 3y = 4 5х + 4y 3D 1

Q: Hw X+22=9 zy +7=8 4X -3y =-2 Aus , X=1 ,u=2 ,Z=Y

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Q: Find (3x + y)dA where D = {(x, y) | æ² + y? 0}

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Q: Find curl (7z i + 8x j+4y k).

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Q: тахz %3D 2x + у S.t х+у<60 2х + у 2 40 y < 30 х, у 2 0

A: Linear programing is a mathematical techniques to optimize solution of given constraints.

Q: f (x, y) = 6xy+ 2x²y + xy².

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Q: 1.y" — у' — 2у 3D 7sinh3t — Зcosh3t ; У (0) 3 2, y'(0) = 4

A: The given differential equation is y''-y'-2y=7sinh3t-3cosh3t; y0=2, y'0=4. Calculate the values ys…

Q: f(t) = 2.4(1.003)*; f(t) = Qoekt %3D %3D

A: Given, f(x)=3e2x This given function is to be converted in the form f(x)=Abx Comparing ,…

Q: 2y+8 2xe to %3D y10)=8= , yco= 2

A: I have solved by using formulas and series expansions.

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: (у + /x2 + у2)dх — хӑy; when х%3D V3, у %3D 1

A: substitute value of x and y in the equation to find the answer

Q: dy 24. Find dr? in terms of x and y. 6-8xy 9x-5y %3D

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Q: 1. ř (t) = (3 – 4t) i + 6t j- (9 + 2t) from –6 < t<8. %3D

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Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

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Q: 2t – 3t2 | (c) h(t) %3D a = 1 1 + t³

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Q: Q/ Find SCZ)dZ Where C:\z-1|-l

A: We use Cauchy's Integral formula.

Q: EX:- Show that dw Vす 2. の ē" dw fcb)-VEerfa) %3D e dw ei

A: Using error function erf(f) .

Q: f m/KJL = (3x + 2)' and mZKLJ= (7x-32)', fir %3D K M

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Q: c. y" – 4y' + 3y = 6t – 8 ; where y(0) = 0, y'(0) = 0 %3D

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Q: y dy J – 1) (y + 4) (2y

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Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

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Q: Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

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

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Q: dx Cane:2e-25x

A: 13)

Q: Given : dy' j + 2k y'î + 4xĵ + 3* Varifng %3D 2.

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

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Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: f(x,y)=(3x^2+3y^2)

A: Given, f(x, y)=3x2+3y2 BOUNDARY OF A DOMAIN :- It is the set of all boundary points of the domain D.

Q: J 5(x) =-J5 (x) ylgn O ihi O

A: See solution below. We used properties pf bessels function.

Q: x(t) = 121? – 12t, y(t) = -41 + 612 + 9t %3D %3D where t goes from 0 to 1. Answer:

A: Solve the following

Q: If (x and jy)² = 3 + j8, find x and y.

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Q: d) xty"- x'y'-(y') = 0, y(1) = 2, y'(1) = 1 %3D

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Q: XY = WZ m22%3D36°, m ZW = 57°, find m23

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Q: 2dt J (t - 3)V2 – 6t + 5

A: Given that: ∫2dt(t-3)t2-6t+5

Q: f(x) = (4e2x)3 3(4e2*)2(4e2x) 3D3(16e**)(4e2*) 192(e6x) %3D %3D %3D

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Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: Show for Re(2) > 1 ez - 1dr = r'(z) 5(2). %3D 0,

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Q: gona u = 2i – 3 j+5k v= 4i -9j-7k

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Q: t(s) y (m) (а) у %3D 1/2gt (b) у 3-1/2gt (с) у %3 1/2g? (d) у %3D- 1/2gt?

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Q: YH = 2x Y HW= 3x – 12 %3D Find YH H W

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Q: dz (z – 5i)3(2 +1+ i)® a) 7: |z – 3i| = 3; 6) 7:z +1-2i| = 4; %3D

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Q: Find v v j 10i - 24

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Q: dæ + 2y¯'¤dy = 2a°y°dy, y(1) = 1. %3D

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Q: Find curl (7z i + 8xj+ 6y k). curl (7z i + 8x j + 6y k) = ( Di + ( j+ ( )k

A: We have to find curl7z i +8x j+ 6y k Now,  curlP i +Q j+R k=ijk∂∂x∂∂y∂∂zPQR

Q: Find curl (2z i + 3x j + 6y k).

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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: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. |

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Q: 9. (D+3D² + 3D+1)y = 0. 13. (4D* +4D³ – 3D² - 2D + 1)y = 0.

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