2t + 3 r(t) -, In(t² + 2) t2 +1

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: z2-ze coshw.K (z) z2– 2ze coshw.K+e2a -

A: The solution is given below. Hope this helps!

Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: (X1, X2) = -x2, Q(x1, x2) = x1; D = {(x1, T2) : 0 < x1 < 1,0 < x2 < 1}. (X1, 82) (¤1, P2) = 2x1 –…

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Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: Мaximize z 3 2х + у За + 4у < 36 6x + 2y < 36 Subject to Маximum is at y = VI VI ЛІ ЛІ II

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Q: 6 - 3x2 + 3 Find the general antiderivative of f(x) - - - x5 + C

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Q: S: z = √x² + y², (x-1)² + y² ≤ 1

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Q: 9-x2 18-22-y2 (x2 + y² + z²) dz dy da? 3 0. x²+y2

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Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 5. y = xArctanx - In v1+x

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Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

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Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

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Q: 3. 2. Z dydxdz 2=0 X=Z

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Q: Q1: Find the general solution of the y - 4y - 5y = 2sin2 x

A: Given differential equation is y''−4y'−5y=2sin2x. We have to find the general solution of the given…

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: z = xy³ – a²y, x = t² + 1, y = t2 – 1

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Q: Мaximize 2 3 4х + 4y || 3x + 7y < 63 6x + 2y < 54 Subject to Маximum is at y = VI ALAL II

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Q: 4. Obtain the general solution (D + D - 9D - Dy = 6e - X 3x + 3xe

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Q: 3x2-3-4e2x and y(0) 8, then y= If dx x3- 3x - 4e2x x3- 3x - 2e2x + 8 x3- 3x - 2e2x x3- 3x - 2e2x +…

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Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

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Q: I(n) = ;n² - 글까-10 5-2t h(t) = t- 1 %3D S(h(0.5)) =

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Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

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Q: (j) z = y² – x² + 2x - (k) x² – y² + z² + 4.x + 2y = 3

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Q: px + qy=z-a √x² + y² + z²

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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

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Q: f(t) = te3t cosh 4t s2-6s-7 А. (s2-6s+25)2 s2-6s+7 С. (s2-6s-25)2 s2-6s+25 3. (s2-6s-7)2 s2-6s-25 D.…

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Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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Q: - Q3): If xfx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n − 1)f

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Q: = (y² – z² +3yz – 2x of the following is/a

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Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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

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Q: 3x The y, of y''-6y'+9y = by using variation of parameters is: .A Y,(x) = -In(x). e 3x 3x -e |

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

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Q: 1. V2 3y 8-x2-y2 رار 0 0 x2+3y2 dzdxdy

A: We have to evaluate the integral.     According to our guidelines we can solve only one question so…

Q: dy 6. S: y3-2y2

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Q: 4 Q1: If y = (x4-3x2) x5-3Vx3+Vx find y' 리x2-2

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Q: 18.t2y′′−4ty′+6y=0,t&gt;0;y1(t)=t2

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