x³-2y2 dy f) dx Hint: You know two methods that will work! 4xy

Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: If fe F- di = Scl-5x + 4y) da + (a*y) dy, what is F? F =

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Q: d. 3) [cos πx]4 %3D dx

A: 3) To find the derivative

Q: If y =√x + √y (a) (c) y + x y² - 2x 3 y³ + x 2y² - x + x + y+...∞, then is equal to dy dx 3 y³ – x…

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Q: f(x y, z) = x2 - 8y5 + z -4. Find (-3, 1, 5) for O a 1 O b -4 10 O d -5

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Q: O SS -İ 2 1 + √√ x² + y² ) dj d x

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Q: 6xy — 2x — 8zx2 = 0 6xy — у — 2zy2 = 0 4x² + y² − 2 = 0

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Q: 1-y2 Q2: Evaluate i y² (x? + y²)dx dy

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Q: /2 ( 2) (2a- z) dr x2) ? dx • B I A , E E E E 8 &

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Q: PLEASE HELP ME ANSWER WITH SOLUTION    18

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Q: Q4 Integrate the following: (a) 4ln|x³| + C x3 dx (b)+C 4 (c)++C (d)+C

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Q: S (Vx² + 1) dx 4 2

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Q: -8y y² + 4xy − 2x² √ - dx

A: We can solve this using given information

Q: e3z I dz (ez + e 5z )2 II

A: Introduction: The Ortrogradsky's method is used in finding integration when the integrand is a…

Q: given f (2) = 3z - 6z+ j3. what is the value of u(3, 2)

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Q: y" + 6y 2+e 1x 二

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Q: 2х + 1 J (x – 2)(x – 3)²ax

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Q: d²x is dy2 15 If x = (3 2y)5/2 , then 15 А. — A. -15(3 - 2y)1/2 В. 2 (3 2y)1/2 C. - (3 2y)1/2 D.…

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Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: 15 -8 -3

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Q: д 2 у б (24)2+ Ady

A: Note: Since, the student has made a typing error in writing the integral ∫012y2y2+1 dy, it should be…

Q: 2х + 3 dx Vx + 2 J 3 4 Answer: (x + 2)7 – 2(x + 2)7 + C

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Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

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Q: Re(ze²), where z = 2-3mi

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Q: S (e3 In = + e3) dx = A. 3 + +C B. + 3e3z + C C. + 3e* +C С. 4 D. + +C 4 e3z E. 주 + + C 3

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Q: Sy-10 y²-4y+11 2. S dy

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Q: make use od auxiliary questions to solve (y²+yz+z²)dx + (z²+zx+x²)dy+(x²+xy+y²)dz=0

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Q: (a² + y²)dæ = 2y[(a² + y?)² + 4x]dy ?

A: First we find the integrating factor then solve this ODE