2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

Q: II. Bernoulli's equation: dy 4. dx -2y %3D글x" xy3

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

Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

Q: 2 Example 10.8. Using Euler's method, find an approximate value of y corresponding to x= 1, given…

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Q: 6. (6x – 3y + 2) dx - ( 2x - y– 1) dy = 0 ans. 3x - y + C = 5 In | 2x - y + 4|

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Q: 10 Find E [Y] = È E [Y|X = a] px (a)- %3D a-1

A: Mean of a Geo(p) distribution is given by, 1p Here it is given that,  Y|X=x ~ Geo(x10) Therefore…

Q: 8-2² y² dzdx dy x+3y 3-3X 3-3X-y dzdyd% SS(x+y+z)dy dx dz

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Q: 1. IT (2, 4) dar dy =/| f(x, y) dy dx %D 0. 0.

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Q: -2 7. (1–xy) dx + |y² + x² (1 – xy)| dy = 0; y (2) = 1 |v² +x² (1 – xy) dy = 0; y (2) = 1 %3D

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Q: 5) (xy² +x-2y+3) dx + x² ydy = 2(x+ y)dy when x = 1, y = 1

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Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

Q: 7.5- yy - 9 4+9) dy -6- 8.S 1 dx e2x+ e-2x

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: 14. Compare dy and Ay for y =x+ 3 at x = 1 with Ar = de-0.09, Give your answers to four decimal…

A: it is differentiation problem.

Q: (х — Зу + 2)dx + 3(х + 3у — 4)dy —D 0 x-1 a. In[(x – 1)2 – 9(y – 1)²] – Arctan C 3 (у-1) | x-1 b.…

A: The differential equation of the form Mx, ydx+Nx, ydy=0 is called the differential equation with…

Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: 4 + 9x x2 The antiderivative of the function f(x) is

A: Solve the following

Q: 3. 4. dy dx xdx x² (y² +³) + y (x³+1) e-x + (Y+) dy y ³ = 0 = 0

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Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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Q: 2 3. (a) Calculate dx. 1+ 4x2 8x (b) Calculate dx. + 4x² 2 — 8х dx. 1+ 4x2 (c) Use (a) and (b) to…

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: 10. (1+e') dy + (x² + 2x + e + y) dx = 0; y (2) = - 1

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Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: y' + 4y = e^(4t) %3D

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Q: 3 d²y If the functions are x = e-t and y = t+t + 1. Determine its dx2

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Q: 18 13 f(x) dz - f(x) dx = f(x) dx where a = and b =

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Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

Q: 3 5. [20 points] Solve (x + y)dx+ dy=0 +x-

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Q: 19 13 f(x) dx – f(x) dx = f(x) dx %3D nere a = and b =

A: Use property of definite integration

Q: 10 10 1 f(x) dx įros. f(x) dx -3 f(x) dx 10

A: First we will find area of each part as follows- The region A1 is a trapezium .So, A1=12×sum of…

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: dv 9. S- V3v-2a 10. S(5 – 3y)*dy

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Q: 5 2 S- 10 Vx+y dy dx 5 2 y dy dx = (28 - 10/3) 10 VX+y 3.

A: given itegralI=∫15∫02yx+y2dydx

Q: x(y-3). * - xly-3) dy = x(y-3)dx nly-31= C y-3 e [y-ce 3 2. Pesticide was given to a colony of 8000…

A: we have been given an equation y'=x(y-3) which can be written as  dydx=x(y-3) here, we will use…

Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: G. q 1-Jx 휴-1 14 314 (x+1) dx 1114 X2 (x-1) X2(x-1) = Anㅎ Sa ㅋ. S? 1+Sx dx=4n 은

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

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Q: Solve: x"-x+ 5 y'=t y"-4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) & L{y(t)}…

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Q: 9. S(9 + 8y – y²)? dy 10. S (e*–2)² dx e 2x + 4

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Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

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Q: 0 1 Q3:Evaluate the irtegals [(x+ y+1)dxdy -1-1

A: The detailed solution is as follows below:

Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: 4. (6xy³ + 2y*)dx + (9x?y² + 8xy³)dy = 0 5. (у2 — 2ху + 6х) dх — (x? — 2ху + 2) dy — 0 When: x =…

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