f (x) = Px = 1 and2 Ox= -1 and - 2 x = 1 and - 2 Px= -1 and 2

Q: Find the particular solution for y' = x3 – 2xy when x = 0, y = 1

A: We are given a differential equation: dydx=x3-2xywith the initial cobdition x=0, y=1 We can solve…

Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: Solve for ∂w/∂y and ∂w/∂x w=(1-2y)(x2-xy)

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Q: Find the particular solution of x²y" + xy' = 1; y = 0 and y'= 1/2, when x=1.

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Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

Q: x" – 2x' + 4x = d(t – 1) x(0) = x'(0) = 0 - -

A: For solving this question we use the table of Laplace transform and properties of Laplace transform…

Q: A. ELIMINATE THE ARBITRARY CONSTANT/S IN THE EQUATION. 1. y= Ae2x + Bxe2x 2. y = Ax² + Be¬* 3. y =…

A: Explanation of the answer is as follows

Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

Q: B. Find the first and second derivatives of i- y =-10x+3cosx+(2x+3)(5x-4x) 5x+1 ii- y= 2x

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Q: Evaluate f- 8x+1 dx V4z-3 (4x – 3)½ +(4x – 3) +c O b. (4x – 3)/2 +(4x – 3)i + C (4x - 3)%2 +(4x – 3)…

A: Given integral,∫8x+14x-3dx

Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

A:

Q: Find the second derivative. 3 2. y = 7x-8x+4 e* O A. 28x-16-4 e^ O B. 16x- 28-4 e O C. 16x- 42 + 4 e…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 2 f(x,у) 3 V9- х* -Зу;B Р(3, - 3); 13 3 13

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Q: -x-1 a) y' = +2yi-1 v(0)=1

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Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

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Q: 2y´´-5y´+3y=0   y1=e^x

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Q: eliminate the arbitrary constant for: y=x^2+c_1 x+c_2 e^(-x)

A: Given y=x2+c1x+c2e-x                               (1) On differentiating both sides, we get…

Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: -x-3 F(x) = S (5t + 2) dt

A: According to question given thatF(x)=∫x3x-35t+2 dt

Q: -4x² – 16x + 2; x # –7 f(x) = {"* -2; x = -7 A. -2 < y< 18 В. у S -2 С. y < 18 D. -2 < y< 18 E. not…

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Q: f(x.y) = 4x - 8x + 5y² + 6; R= {(x.y)(x= 1)² +y² s1}

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Q: e) xy+ y² = 1 f) x2/3 + y y²/3 = 1 g) x3 + y4 = 16

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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: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: (xy+ 2)* - 3x+e" =e C.

A: Part 18CGiven,           xy+22-3x+e-y=e-x

Q: Eliminate the arbitrary constant/s: y = Ax^3 + Bxe^-2x

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Q: px + qy=z-a √x² + y² + z²

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Q: ze² dz (1+ x)* + C 1+ z

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Q: Find the general solution of 2y"+3y+y=3sin.x+xe"

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Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

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Q: Verify that for x>0, (2/ /3)x³² 2 is a solution of the equation yy" =x.

A: Given:     To verify: y is the solution of equation yy''=x

Q: Differentiate: y = x2 + 3x – 1 x2+1 A. x2+3x-1 -(x²+1) В. (x²+3x-1)2 -x2+1 x2-1 С. (x²+3x-1)² D.…

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Q: f(X) = %3D Vx-2

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Q: max x+ y2 + z² subject to x2 + y² + 4z² == 1 and x+3y + 2z = 0

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Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: 1. -(3X)(Px v Qx) 2. (x)(Sx• -Qx) ɔ (3x)Px | -(x)Sx

A: We have to prove the given arguments

Q: H.W. Xdx 1-- 1+3X2

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Xyz = 0 12. Solve: {x+ 2z = 1 2y-z 4

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Q: 3 18. z= 19. y= Vx(x-1) 3x-1 20. y= 2x+1

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Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: f(x) = { Sx + 2 1-x+3 x>-2 Dano

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Q: Find the particular solution of (d2y/dx2) = 4x3 - 2x; y' = 4/5 and y = 1 when x = 1

A: Given differential equation, d2ydx2=4x3-2x       ...(1) y'=45 and y=1 when x=1

Q: Solve for the derivatives. For 16-20. y = -7x5 + 3x3 – 2x а. 35x4 — 9х2 + 2 b. 35х* + 9х3 + 2 с.…

A: Disclaimer-Since you have asked multiple questions, we will solve the first question for you.  If…

Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

A:

Q: f(x) = é ーx46x? J6-6x -6 A) e-+6z² (-6x³ + 12x) + 2/6 – 6x Calculate f (x) 1 2/6 – 6x B) e-+6z°…

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

Q: Find the derivatives of the given functions. (Part D and E)

A: d)  We will need the quotient rule. For that assume u and v and find u' and v'