16 : = 16 – x² – y? 2 y = 4x – 2 y = 2Vx

Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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Q: 3) Evolvate Ci(0) e²/z dz е

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Q: dy Find for the following by using appropriate rules: iv. x² + y3 + (lnx)e♥ = 4. y = Vx(3x2 – 1) V.

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Q: - y² + 22 = 169 at (5,0,12). %3D (1) . i+3 3 3 -) i+ k, 6. 12 12 =) i+k, (d) k. i+

A: In this question, the normal to the curve is calculated using the finding gradient of the function.…

Q: 1 dz (z + 1)°(2:² + 4z – 34)i

A: Solve, as follows:

Q: 4. Find y' where y = – 1)^(2x – 1)3

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Q: 1.y" — у' — 2у 3D 7sinh3t — Зcosh3t ; У (0) 3 2, y'(0) = 4

A: The given differential equation is y''-y'-2y=7sinh3t-3cosh3t; y0=2, y'0=4. Calculate the values ys…

Q: (2siny + 1) = 4 and y(0) = what is x when y =n?

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Q: If y = (x? – 4)2 - 2arc sec find y'. 2' Vx² – 4 Vx² – 4 1 Jx² – 4_ 1 4 A. В. C. +- D.

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Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: Find dy for given Values OF x and AX y= 4x315x X=-3 and AX = 0.3

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Q: z2 = 9 and outside the cylinder x? + y? = 1.

A: coordinates, x=r cos θy=r sin θz=2 x2+y2=r2cos2θ+sin2θ=r2x2+y2+z2=9r2+z2=9⇒z=±9-r2 x2+y2=r2⇒r=2

Q: How do I integrate the following equation? U(z)=2.8*exp(-z/6300)

A: Consider the given equation as Uz=2.8*e-z6300

Q: w=z/3y−x, solve for y.

A: The given equation is

Q: 14. yy +x =Vx² + y?

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Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: Solve for x and y. X = y = 17 1 5x + 20 5 [723]-[2725231 2y 1

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Q: ху? + х — 2у + 3)ӑx + x?ydy %3 2(х + у)dy, when x %3D1, y %3D 1

A: Answer and explanation is given below

Q: Į va | Vi(t? + 6t +7) dt. 4. Find

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: 7. y = sec x, y = V2, -TT/4 sxS/4

A: y = secx , y = 2,   -π4≤x≤π4

Q: 3 Evaluate 2z (4 – a – y) dy dæ.

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Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: dy 4. x2 + y? = dr xy (Bernoulli DE) %3D

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: dz wher the integral fe z2 +9 C = 4 is

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Q: eY+Ve2y-4 5. x = In sove for y“ 2.

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Q: 1. x = y =. M 31 L5y9

A: Triangle properties

Q: Q1: Find the value of constant (K) 31 k xy#e* dydx = 56 %3D 27 0

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Q: 7. y Vzy dz + dy = 0

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

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Q: + 12D + 36)y = 0 5. (D³ + 3D² + 3D + 6 (D3 AD3

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Q: 2 V4-x2 e*²+y* dydx =? -2 0

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

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Q: If  z = 3x2 + y2  and  (x, y)  changes from  (1, 3)  to  (0.95, 2.9),  compare the values of Δz…

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

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: 11. (D³ + D)y = sec? x when x =- 4 = %3B

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: v x +y = 2xy + 4x; at x = 1 and y = 3

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: Solve y"(t)- 2y' (t) + 5y(t) = H(t); y(0) = 0; y'(0) = 1; where H(t) = (t+2,0 ≤t <2 2t - 3,122

A: We have to solve by Laplace transform.

Q: (2t – 4 Ost<2 (D? – 1)y = 2 t22 у(0)-0, y'(0)-1 Find L{y}

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: Ex3) show That y= ē" is Solution Lor y+y`-2y=o

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Q: dy y2+1

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: f (x, y) = 3x² + y³ + 4xy² + 8 What is the value of df (x, y) dy when x = 2 and y = 5?

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Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: 2. Given y = 25e-2x verify that y' + 4xy = 0 Your answer

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Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A: