2/3' 2/2, Suppose 3z? + 2y² + z² = 1 and z = g(x, y) > 0. Determine g, ) and gy 2/3' 2/2

Q: " Show that the substitution JAx + B| = 'e², or z = In |Ax + BỊ, will reduce the equation dy a(Ax +…

A: I have used the given substitutions to reduce the equation

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

A:

Q: graph of (x) = x' - 2 is shown in the figure. Find 6 such that if0 2 ]x - 4] 2 8, then IAX) - A. ô =…

A:

Q: Find dy/dx given xy2 + x²y5 – x³ = 3 %3D -

A: Given that : xy2 + x2 y5 - x3  = 3. Find dy/dx . We know that d(xn)/dx = nxn-1.   Here i attached…

Q: The equation (x*y^2 + x – 2y + 3)dx + (y*x^2)dy = 2(x + y)dy is not exact. a. True b. False

A:

Q: J(1 - 4x4 +x)/x dx = 1/(2x) + 2x2 -x +C Select one: O True O False |(4csc?x-3sec2x) dx =…

A:

Q: (x – y)(4x + y)dx + x(5x – y)dy = 0.

A:

Q: 6 2 5x y 18. 10x* y

A:

Q: 13.9y" +12y + 4y = 0, y(0) = 2, y'(0) = -1

A:

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: y*dxdy V2 y у?)2 2 3/2 (x² +

A: Here we have to evaluate I=∫01∫0yy2dxdyx2+y232=22

Q: 5. (1-x) (dy/dx) + xy = xy". Ans. cy=(1-y)√(1-x)

A: Given equation is 1-x2dydx+xy=xy2. To find: solution of the given equation.

Q: 7/12 16.r(sec 4.r) dr =?

A:

Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

A:

Q: 3+6z²+3z+6 dr z+2z

A:

Q: dy Q2) Solve x- 2y = x³ cotan 2x dx

A:

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

A:

Q: The roots of the characteristic equation of y"-7y=0 are:  a. √7.-√7  b. 0, 7 c. 7,7 d. 7.-7

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

Q: i) P(5, 25) belong to y = x, what will the point P be transformed to after the equation transforms…

A: Real valued function

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: 6) y' 2.x-3y+4 x+y+2

A: Answer

Q: If u(x) = x3, then du = 3x2.

A:

Q: 8 If x2 = 25 - y2, what is the value of dx2 a²y at the point (3, 4)? 25 (A) - 64 (B) - (C) (D) (E)…

A: use the quotient rule to find the second derivative.

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: 2. +x +1 d

A:

Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

A:

Q: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the constant values of m and n if 2y = 2nx² + 2mx given that when x = 1, y _0 and = 14. dx

A: