6x +5y find ху - 8 dh and For the function h(x,y)= dy dy

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: d²y Find dx2 for the function x²y² + 6xy 17 at the point (2, 3)

A: First find the first derivative at that given point than take the second derivative.

Q: 2t2 3t and X = 1-t d²y| Let y . Find dy and 1-t dx dx2 It%3D4

A:

Q: Find df/dx and df/dy for the function.  f (x, y) = 2x2ey

A: given:  f (x, y) = 2x2ey

Q: 2t -4 0st<2 D2-1)y= t22 y(0)=0, y'(O)=1 Find L{y}

A:

Q: 3x + 2y find 6xy -7 ah For the function h(x,y)= %3D I3I

A: The solution is

Q: f Gx,y) x+ 3 XY %3D

A: We have to check

Q: Solve y" + 2y' + 2y = g(t), y(0) = 0, y'(0) = 1, where %3D %3D S1 0 0 27 T <t< 2m g(t) =

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Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: function 3y + 1 + y = 0, is: %3D

A:

Q: Q3. Solve dy (x+3) dx S 3x, 0 3.

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Q: f(x, y) = 1 + x2 - y2 R = {(x, y): x2 + y2 < 1}

A: Find the area of surface given by z= f(x,y) that lies above the region R.

Q: I'+yz² -2xyz = f(x*y+y*z+z*x)

A: Given:- x3+yz2-2xyz=fx4y+y4z+z4x

Q: Solve Xy"-xy' +y = a+3ln(x), y)=Q , yl)=1 %3D

A:

Q: 2. b. Then, use the linearization to approximate the number V8.7. Be sure to show work, and clearly…

A:

Q: 2x X 5) i dydx y 1 x

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Q: f (x) = x² + 6x if x = 2 and dx = 0.3, determine dy

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

A: Given

Q: Obtain the second derivative of the function: y = 2 – 5x4 + 3/2x2

A: Since this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: Y1 (t) = 2t – 3, y2(t) = t² + 1, y3 = 2t² – t, y4 = t² +t +1 %3D

A: We will find out the required solution.

Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

A:

Q: 8x - 2y f(x, y) 7x² + 5y a² f dy? dxðy dydx

A:

Q: (3x*-5)(2x +9x-6 of y= dy and %3D Determine the 7x

A: Simplify the equation. y=6x7-10x3+27x5-45x-18x4+307x5=67x2-107·1x2+277-457·1x4-187·1x+307·1x5

Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

Q: t² - t dt 0, = (x)6 g'(4) =

A:

Q: ey - x+y = 10

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Q: f(x) = x² + 6x if x = 2 and dx = %3D 0.3, determine dy

A: f(x) =x^2+6x

Q: Z-f(x,y)= 2x- 2xy ty 2. 2x<y54, 0く×<23 Find absolute max and min

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

A:

Q: Find the linearization L (x, y) of the function f (x, y) = V101 – 4x2 – 9y? at (-2,-3). L (x, y) =…

A: In the question it is asked to linearize the function f(x, y)= 101-4x2-9y2 at (-2.-3).

Q: y'(t) = y sec t, Y 6) = 0

A: We need to solve the initial value problem y'(t)=ysect ; y(π/2)=0. The solution is given below.

Q: REDUCTION OF ORDER AND VARIATION OF PARAMETERS 1. (D² + 4) y = tan 2x 2. (D² + 8D + 16)y = C. 1-e4x

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Q: Find the function​ y(x) satisfying d3y/dx3=36, y′′(0)=14, y′(0)=5, and y(0)=8.

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Q: 4x + 9y For the function h(X,y) = 5ху - 3 find and дх dy

A:

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: Revenue function is given R(x,y) = 19+162x+210y-3x2-5y2-6xy  , it is function of two variable…

Q: ly₁ dr dy₂ 2t = y₁ + 4y₂ + e¹t - e²t = y₁+ y₂ +t+2

A: given  :         dy1dt=y1+4y2+e4t-e2tdy2dt=y1+y2+t +2 We have to solve the given system of…

Q: Decide whether it is possible to solve the equations xu? + yzv + x²z .xyv³ + 2zu -- u?v² = 2 for (u,…

A: 3.7 Given equations are xu2+yzv+x2z=3xyv3+2zu-u2v2=2 The points are  (x, y, z)≈(1, 1, 1) and  (u,…

Q: 2x2 f' (æ) = If f(x) = V 1+t° dt, then

A: To find the derivative of integral apply the follow rule

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: Solve. y'(t) = 2e^2t(c1cost(t)+c2sint(t))+e^2t(-c1sin(t)+c2cos(t), y(0)=0, y'(0)=1

A: General solution of the differential equation

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: f(x, y) = x4 + yA; x2 + y2 = 18

A: In this question, we find the maximum and minimum value of the function by using the Lagrange…

Q: y(2x- xy ty')da-x (2x-y) dy =0, when x(4):0 %3D

A: Given: y(2x² - xy + y²)dx - x²(2x - y)dy = 0, when x(1/2) = 0

Q: 2s -5t f(s,t) = %3D 4s +t %3D f =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: V2 r8-x²-y² •3 Evaluate: 1 dz dy dx x²+3y2

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Q: Ly 2r 7. J. y -2r K. y 2x 8. 11. 12. 13.

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Q: V4 – a2 - x2 valuate f, S Sva-a - ° ( + 2²) kz dz dy dæ – a2 – 3y? (y + z2) kz dz dy dx

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Q: Q1: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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Q: -1 df For the function Y = f(x) = x² + 2x + 4, x > – 1, find dy y=7 (f-1)'(7) =

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.