1 2 _2 If U= +¯ +y¯ +z¯ is not equal to 0 then prove x+y° + dU + du that dx = 0 dx dy

Q: 1. (e + In y +) dx + 2 y + Inx + siny) dy 0

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Q: 2 Solve S dy Use u substibation with u=y² ¢ CLearLy show gamma function r (n+2) = nTn) propeaties

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Q: 3 3 4 Evaluate the integral S [(?+y?+?)dz dy dx. 0 0 0 3 3 4 S[?÷+²)dz dy dx=O 0 0 0 (Type a…

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

Q: Solution for the initial value problem using laplace transform y' +4y =cos(t); y(0)=0

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Q: DE 1. (-x)y-4xy +5y = cosx 2. d²u d'u 2x² at³ 3. d³x 12 des -2 d²x +(4t-1). + sin t dt² 4. √1+ (v)³…

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Q: (X-Y 4) Calculateſſ cos dX dY about the region E: X+ Y = 1; X+ Y = 4; X = 0 ; Y = 0 X+Y 15 15 sen 37…

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Q: (e² + In y + ) dz + (; +Inz + sin u) dy =0 2ta Iny+y ln z-cos y C O e² - = C a Iny +y ln z+ sin y

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Q: 1 4 1 Evaluate the integralI| «? + y² + z²) dz dy dx. 0 0 0 1 4 1 SS 2+y? +z²) dz dy dx =| 0 0 0…

A: In the given question we have to evaluate the integral Method: first of we integrate the integral…

Q: dy dt (d) di² + 2- 3— 3t + 2, у(0) — У (0) — 0. dy (е) di? dy + 20y %3D —3 sin 2г, у(0) %3 у' (0) —…

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Q: 2-x Consider the integral [ff av = √₁² √²-²² √²-* [[ [* dV 0 0 S (a) Sketch the solid S. dz dy dx.

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Q: 19 271. dx y= 1-X) dy = -Ldx -dy= dx S-(-yei) y" dy 99 99 100 100 99 dy dy 100 %3D + R00 100 ). %3D…

A: Refer below

Q: 5. Find fSp(x + y)² dx dy, wh- region in Fig. 17.2.12. y = x

A: Answer is 7/12

Q: ) oe.no dy en x = 0-1 of the IVP = x² +y, y(0) = 1 %3D %3D dx s method. Iving the

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Q: The length L of a line on a sphere of radius r between two points, specified in the spherical…

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Q: S f(x) dx = 5 ve 8(y) dy = 7 olsun. R = [0,2] × [2,3] olacak şekilde %3D %3D I = SSrf(x)g(y) dA…

A: To find the solution of double integral.

Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 2х- 1 dy for y = dx J (*-7) (1* -7) dt. Use Leibniz's rule to find dy dx

A: Given, y=∫02x-1t4-7dt Using Leibniz's rule we have to find dydx. According to Leibniz's rule we…

Q: I need help with 1a)

A: straight line becomes y=x

Q: 5. Use the separation of variables method to determine the solution u(x; t) of the heat transfer…

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Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: -+y= cos 21, y(0)= 5 dt y(0) = 5 %3D

A: Thus solution is

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: 10. If µ(x, y) of the the DE. x" y" is an integrating factor (12 + 5ху)dx + (6х у-1 + 3х?)dy %3D0…

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Q: 5. Solve the initiał vałue problem: dy 5. dx + sin(x), y(0) = 1 %3D %3D 1+x2

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Q: Question 1. d²x + dt² Classify the following differential equations Equation 2 - cos 3t = 0 d²r de…

A: Note: As per company guidelines we can solve maximum three sub-parts at a time, So we are solving…

Q: Which of the following differential equations is exact? O (cos xy + xsiny) dx + (y – cos x + sin y)…

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Q: 3 13. If x = u + v³ and y = uv – v² are solved for u and v in terms of x and y, evaluate ди ди dv dv…

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Q: dy Use 4th order Runge - Kutta method to integrate step size of h = 0.5 and an initial condition of…

A: Let dydx=f(x,y) and the initial condition is y0=f(x0) . The 4th order Runge-Kutta method uses the…

Q: 2 1 Evaluate the iterated integral42x°y® dy dx. 56 -1 0 2 1 | 12*y®dy dx= [ -1 0

A: Consider the integral

Q: y 1) x(In x – In y)dy – ydx = 0 Ans: = c (Xie, 2010) %3D 1+In y-In x

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Q: ii- 2(2 cos y dx – sin y dy) = 0. y(0) (using Integrating Factors) = {) %3D

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Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: 31. (1+ y cos x) dx – sin x dy = 0 - 32. (sin? y+ x cot y) y'= 1 33. dx – (y- 2xy) dy = 0 34. dx –…

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 15- dy _y* -x diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? 2ху dx x-y' =cx 046…

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Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: Can you please check my work for question 14? I know it it hard to follow, but I don't know if I got…

A: The given equation is,

Q: Solve the initial-boundary value problem Utt = 16uzz u (0, ) u(π, t) 0 u(x,0) = E sin(nx) u:(x,0) =…

A: ∂2u∂t2=16∂2u∂x2u=XT . . . . (1) Where X and T are function of x and t. ⇒∂u∂t=XdTdt,…

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0…

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Q: n/3 CoSx dx dy, If we reverse the order of the following integral : cosx we get: Select one: siny dx…

A: The given function is  F(x)= cosx/ x

Q: 9 1 [y sin x dx dy 0 0 What do we get if we write the integral with the variable equation = Vỹ , v=…

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Q: Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln…

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: b) Evaluate the triple integral S dx dy dz re3 1 xyz

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Q: the separable Pential equation dy In(x³) dx ху subject to the initial condition У(1) %3D —3.…

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