%3D iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+ y) d.z² (x- y) a.x-y

Q: y = = Vx, 1s xS 8 Intograte ith

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Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

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Q: d by f(z) = (x alytic, then C %3D

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Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: y = 8e*, on x e [0, 2]

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Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

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Q: 4. у" — 2у'+у %3D хе* — е" x’e* Ans. y= c,e* + c2xe* + 6. x²e* 2

A: Solution

Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: y" + ay' t sy = g e-2^ + 8 %3D ylo) ay'6o) =

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: Q2 Given that z = 8x2y - 2x + 3y, x = u v, y = u – v %3D az az and ди Find av

A: To find dz/du and dz/dv.

Q: (D^3 - 2D^2 + D) y= xe^x + 1, y(0) = y'(0) = 0, y''(0) = 1. By inspection method.

A: We are given a third order non-homogeneous linear ordinary differential equation as : y''' - 2y'' +…

Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

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Q: الرابع: جد ناتج احد التكاملين التالي ين 1- Smte) xy e*y° dxdy 2- r? N4-y² ry8-x²-y" zdzdxdy x²+y2 2-…

A: 1 ∫01∫0ln(2)xyexy2dxdy first we will solve ∫0ln(2)xyexy2dx ∫0ln(2)xyexy2dx=y∫0ln(2)xexy2dxSubstitute…

Q: %3D 3. If GH = 7x + 18 and JK = 81, find x. H G 丰 K 廿 世

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Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: Find EF in the trapezoid. A 4 D E 2x+6 5x+4 EF = %3D

A: Find EF in the trapezoid.

Q: If F(x,y, z) = 2x² + xyz – y²z a²F :? Q14. %3D xz – 2yz -2 -2z 4x + yz What is-

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Q: 4yy" + 2y' = 0 = y' =? A) y'= -In B) y' = In c) y' = 2n(cy) D) y' =-In E) = 4 1n

A: Given that 4yy"+2y'=0

Q: The mgf. of a r.v. X is (}+3) (+e) . Show that 9-x Ρ(μ- 2σ<X<με 20 - Σ (!) ( (3) P (μ- 2σ< <μ+…

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Q: 5. Differentiate the following a) y = e*(x³ + 4) %3D b) y= x³e* 3 у %3D et c) у%3 x2

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Q: 3 Evaluate 2z (4 – a – y) dy dæ.

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Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

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Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: W = / x2 + y² + z² Find Wx, Wy, Wxz,Wyy, Wzyx %3D

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Q: y with i W1 merically

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Q: 3x²y if (x, y) = (0, 0) + y? if (x, y) = (0, 0) f(x, y) = { x +

A: In this question, we have to check the continuity of a function of two variables.

Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: 2 Find z ax? 2 and ду?. ay ax 1. Z z = 3x y³ 4x* y?

A: Here I am attaching image so that you understand each and every step.

Q: 4. Y= C, ex + C2e* + X

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Q: Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

A: Explanation of the answer is as follows

Q: E(x,y) = 3x²+2= -6x+ &y+I6

A: Finding the critical points of the given function

Q: Find the domain of y = vx+6. %3D 12. O x 2 6 O x > 6 1/6

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Q: %3D Given: 40 elx [y"-y'] = (x+1)(1-e'2X); determine; А) Ур В) Ус

A: Given 40eixy''-y'=x+11-ei2x

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

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Q: SIL- W : x² + y} < 9, 0<z<6

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Q: 1 If Y = x? dy = ? then dz · +c O 22? O 2x 2 dy If y = 6x + 2.5x² + 7x + 2 then dr

A: 1. Given y = x2 So dydx = ddx(x2) = 2x Answer: 2x

Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

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Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

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Q: a2z + əx2 a²z If z = In(x? + y²), find ду?

A: Find ∂2z∂x2+∂2z∂y2.

Q: Calculate ∂ω/∂z for ω=e -2xe((z^2)y)

A: While calculating partial derivative ∂ω/∂z, all other variable except z will be considered as…

Q: Determine c1 and c2 so that y(x) = c1 e^2x + c2 e^x + 2sin x will satisfy the conditions y(0) = 0…

A: NOTE: Refresh your page if you can't see any equations. . the given solution is…

Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

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Q: 2x³y' = y(y² + 3x²) using Bernoulli.

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Q: 2.2 nd, from first principles, fa(3, –1) for f(x, y) = 4x²y² + e®. |

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Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: 3x d.A, A= {(x; y) E R² : y E [0, 1], x € [y, e®]} .

A: Given: A double integral ∬A3xdA, A=x;y∈R2:y∈0,1, x∈y,ey ∬A3xdA=∫01∫yey3x dxdy=3∫01x22…

Q: fud the general Schiklen for the P+q =X+Y+Z

A: p=dzdx and  q=dzdy Let f(x,y,z,p,q)=0We can relate this equation to F(x,y,z,p,q)Then we have the…

Q: Find dy for the given values of x and Δx. y = 6x3 - 7x ; x = -3 and Δx = 0.3 .

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Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-