2. If Ā = ê + ŷ, B = 2â – 3ŷ + 2 and C = 4ŷ – 32, determine %3D (a) (Ã × B) × Č (b) Ã× (B × Č) Comment on your answer.

Q: Find e* + x-2 + C e* – 1+ C + C (1/2)x² e* – In |x| + C

A:

Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

A:

Q: Consider the equation E : y² = x° + 8. Compute 2P and 4P for P = (1,3).

A: Given clear explanation below

Q: Solve the Leontief production equation for an economy with three sectors, given the following. 0.5…

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Q: 1 7) Find the antiderivative: S 3x2-6x+12

A:

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

A: Solution

Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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Q: What is the product solution of the PDE ax = 0 ? ay a. Ae*+y b. Ae*-y c. Ae(x+y)k

A:

Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: (D2 — 4D + 4)у — еЗx A. y = cqe2* + cze2x + e3x B. y = ce2* + c2xe2x + e3x C. y = ce2x + cze2* +e 1…

A: to find out the general solution of the given differential equation

Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

A:

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

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Q: let x= et then by the chain rule d3x/dx3 equals

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

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Q: 6. S Se(x² + y³)drdy, wherein B = {(x, y) E R²; 1< x² + y² < 4}

A:

Q: 1. y" + 4y' + 4y e-2x x2

A: The given differential equation is: y''+4y'+4y=e-2xx2 Now the characteristic equation of the…

Q: Which of the following is one of the correct steps to differentiate y=(3x-2)2(2x-3)3 ?…

A:

Q: 3:30 A3. If y = e2x+5 then y' = %3D LA) 2e2x+5 (b) e2x+5 (c) 5e2x+5 (d) e2

A: Given query is to find the derivative of the expression.

Q: (t5 + 1)dt dp 3.

A: ∫3xt5+1dt =t66+t3x =x66+x-366-3 =x66+x-2492

Q: d (d) (e +2x)°] = 3(e + 2x)² (eª + 2) dt

A:

Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: Find a particular solution to y" + 6y' + 9y = 3z e

A: We use the method of variation of parameters to find the particular solution to the given…

Q: If we substitutev = 2x + y in the D. E y + 2x + y + 2 = (2r + y) e we obtain :

A:

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

A:

Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

A:

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: The chain rule of antiderivative is stated as: ff (g' (x)) g(x) dx = F (g(x)) + C True O False

A:

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: 2 da x² – 8x + 17 Integrate: + C

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: [E (XY)P SE (X²) E (Y²)

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Q: 3 dt (d) 4+ 3t2 -2

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Q: (d) Find E(Yk) - Y(k-1)), 2 <k<n.

A:

Q: 1. If rxty = +1 and rx2y = -1, can you tell what happens to ry when we combine x1 and x2 into a new…

A: The correlation coefficient is used to calculate the linear relationship between 2 variables.…

Q: ral of the d D- 1)y is

A:

Q: What is the product solution of the PDE-= 0? Bxe ay a Ae*+y b. Ae y C. Ae+y)* d. Aex-y)* e. None of…

A: We have to solve given problem:

Q: (c) 부3D . Yk+1 k+1 Yk k

A:

Q: Find general solution of the DE 4x2y′′ + 8xy′ + y = 0

A: Consider the given equation. 4x2y''+8xy'+y=0 Let substitute the value is y=xm. Now, find the…

Q: 4) Aşağıdaki fonksiyonlardan hangileri a2 əx² 1 a2 v² ət²! dx2 dalga denklemini sağlar? Neden? a) f…

A: a) Given that f=5x-5vt3 Now, differentiating f with respect to x, we get  ∂f∂x=35x-5vt25=155x-5vt2…

Q: R - TVE + Vicsc(t) dt e tan (e) dr Vsec (e-) – 7 82y²-3g° (y² – y) dy

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Q: So Ve Pollowing the D.E 3X 3y' = e - \2 X +39

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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: If FX) is an antiderivative of x+ x. then what is the value of A(1) - A-1)? (A) -1 B0 -2

A: Finding F(1)-F(-1)

Q: Use the Gauss-Seidel method to solve the following system until the percent relative error falls…

A: The gauss-Seidel method uses the iterations to solve the system of linear equations. The iteration…

Q: 19) If y- find the value of yl.3y. 3' A) 3. C) 1 B) 0 D) 3

A:

Q: Q2. If the solution of the below first order D.E is y = C ef(xy) (x³ + xy2)y' y3 Find the f(x,y).

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.