Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

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Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

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Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δt =0.006t2. At time…

A: According to the given information, it is required to determine the value of m.

Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: 6. If f( x, y) = V x° + 1 y², estimate the value of f( 2.06 , 4.97 ) using the differentials.

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Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

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Q: d csinx 1 dt 1-t2 dx '3 V5 SNt VE2 + 1 dt 1+xv

A: We have to solve the integral

Q: 5. Given that 8x2 w(x, y, 2) VIVE Use partial derivatives to find the maximum percentage error in w,…

A: Given, w(x,y,z)=8x2y3 z4Percentage error in x, y and z is 1% , 3% and 4% To find: Maximum percentage…

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

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Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: V Solve usıng variaton of parameters or reduction of order (D²+1) y = tan

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

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Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

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Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

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Q: ne differential ay of 'uonpuni y = V 5 - x2

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