make the given substitutions to evaluate the indefiniteintegrals. ∫12(y4 + 4y2 + 1)2(y3 + 2y) dy, u = y4 + 4y2 + 1

Q: Find the laplare transfurmution of the followsng 3X+3y +5X = 25 Cost , X(0) =2 %3D 2x'- 3y' = 5 Sint…

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Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: 5) Compute J(x²+y?)dxdy, where D is the intersection of c irc les r=2 cosg and =2sing.

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given data:     The expression for the given electrical potential function is: V(x,y,z)=3x2-2xy+xyz.…

Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: 6. Use Green's Theorem to evaluate (y- ry') dr + (2- r) dy where C'is shown below. x +y =

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Q: find the geeral aluten for d'y dy du Ay= eax (1+u*) du2

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Q: Given: y = f(u) and u = g(x), find dy/dx: %3D a) у %3D сos u, и%3D—х/3 -x/3 u = b) y = tan u, и 3D…

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Q: 1 Evaluate J JA Totu2)2 dxdy, where A is determined by the conditions 1< x² + y? < 2.

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Q: Evaluate the followingintegrals.∫(z+1)√(3z+2)dz

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Q: find the general solution of the following 2. X Ux +y Uy +t Ut =xyt %3D

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Q: Transform the equation dy = ry into a variable da separable form. O vydy = xdx dy dy Vydy de %3D

A: We will transform the given equation into variable separable form as shown below

Q: F ind the oua gohenegion Aounded ky メ=y,メ=13-が 2 x=18-y (0,9) てっ (,) Une borizontal ilement to firid…

A: The area of the region can be calculated using the formula , where is the curve of the first…

Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: Find u+ Hy:given that u(x,y) s tan(x+ux+ 11y") 11- x2-y?

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac…

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Q: 3. Show that the equation for G(r,ø) can be separated by choosing G(r,ø) = R(r)P(ø) into OR Rar ar 1…

A: Introduction: The Laplace equation is one of the most important partial differential equations. It…

Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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Q: 41. In each part, confirm that the stated formula is the local linear approximation at (0, 0). 2x +…

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Q: is T Mzxz Mzuz defined by T()=(* ) in vertibla? If so hind Q tb C td its inverse T-l thet is find…

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Q: Transform the equation (ry? - z) dz + (z²y + y) dy = 0 into the form of separable dit %3D O ( + 1)…

A: Question is solved.

Q: By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R…

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Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to th indicated value. y' =…

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Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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Q: 2t es the given condition; r' (t) =i+ te-t"j - =k;r(0) = i %3D t2+1 Vt2+4

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Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

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Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

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Q: ürkçe: f(x, y) = 4 + x° + y° – 9xy fonksiyonunun yerel ninimum değerini bulunuz.

A: Please refer to the image below

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: DE DF EF 11. Given: GH Prove: ZE E LH GI HI DE 12. Given: GH EF ; LE = LH HI E H. EF Prove: HI DF…

A: Given: ∆DEF and ∆GHI DEGH=DFGI=EFHI

Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.