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

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: dy Assuming - 2x³ + 8y² + 6xy = 0 defines y as a differentiable function of x, use the theorem dx dy…

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Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: integral f y^2 e^5y dy

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Q: s2, y'(0) = 0 where/burada h(t) to, 0 <t<1 y" – 2y' + y = h(t), y(0) = 0, %3D %3D t21

A: we have giveny"-2y+y=h(t)   y(0)=0  y'(0)=0where h(t)=2  0&lt;t&lt;10       t≥1first find…

Q: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…

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Q: d"y Q5 dx * - 5 d³y +74 – 3y = 20 sin(x), y(0) = - 1, y'(0) = 2, dx use the method of Variation of…

A: This is 3rd order first degree non homogeneous ordinary differential equation.

Q: (c) t? dy + 2ty = cost , y(T) = 0, t > 0. %3D dt

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: 27. w = ry + yz+ za, x=r cos 0, y=r sin 0, z = r0; dw dw when r = 2, 0 = 1/2 dr' de

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Q: ²+ re" = 2y + e² %3D

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Q: riable t. If 2sin (x)+4cos(y)=3a dy and dt 3, what is the val

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Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: tle dettes enti al equation a 9y + Çt 99 +12y =0 dz oaly independent colution Of tle foam y= x"

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Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: ;(y+ 1) e*dx = (e* + 1)y dy, what is F = 1.F. J (-e*y - y)dy? %3D

A: Given: y+1exdx=ex+1ydy

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: 4хy + 5y? xy +3x? in x and z by using the substitution y = xz dy = can be transformed into a…

A: We will use the substitution to try to transform the given differential equation into separable…

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: ORDER DEGREE LINEAR OR NON- LINEAR x*y" + xy" = e* (y')? – 3yy' + xy = 0 d2 ds t dt t2 = 1- sint dt?…

A: See the details solution in below

Q: d²y dr +24 -52y=0; y(0)=; v'(0)= ; y'(0): dt Use Rod.uction ofE Ordor 3

A: Explanation of the solution is given below....

Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: Q1\ Use Runge-Kutta method with (h=D0.1) to solve the equation y+ 3xy - 6y = 0 ; given that yo = 1…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (ztan 2 +1) dx – x dy = 0

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Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

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Q: Find the yacral Selution Sulution 2. d 2. dy +y=D0

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Q: y" +2y' + y = 2 sin t H(t – n), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e- [cost + (t+1-)e™-"]H(t-n)

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Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: f x = sec(z) and y = tan(z) , then dy at z = dx 4

A: We can use the chain rule of derivative in order to solve the given problem.

Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: S(r* +x )dx Approximate with n = 4 using Simpson's Rule Trapezoid Rule.

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Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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Q: 4. (x + Vy? + 1)dx-(y y-: dy = 0 Vy2+1, %3D

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Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: f(x) = 3x²+x+7. Approximate fo trapezoids. O a. 60 Ob. 44 Oc. 30 Od. 22 f(x)dx using the trapezoidal…

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Q: 2 -πx²y. = The volume of a right circular cone of radius ï and height y is given by V 3 dy when x 4…

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Q: dy If y = f(x) is solution of dx? = 0 with the dy boundary conditions y = 5 at x = 0, and at x = 10,…

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Q: C:x=t4, y =t (-1<1< 1) 25. -ydx +x dy C : y² = 3x from (3, 3) to (0, 0)

A: First I have change the line integral into single variable using the given path and taking limit…

Q: dx dy Explain your solution to the problem: = x + 3y – 2t², 3x +y+t.+ 5 dt ||

A: Given the system of differential equations:              dxdt=x+3y-2t2                  ......…

Q: dy 2 %3D (1+x 3 dx 2 What is the value of k such that y is perpendicular to the curve y = 3x + 1 at…

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Q: valus

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Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: sec y Then y8 Let z dz dy y16

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Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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Q: 2x? dy 2 - y dr dy = cos z dy x + y dr dy 3x O dy E = y (2 – y) ||

A: The given options are  y'=2x2          (1)y'=2-y         (2)y'=cosx       (3)y'=x+y…