dz 6. [0]. z-a

Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: 5. +xy+y =3 at (1.1)

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Q: Higher Order L.D.E (D2-2D+10)2y=0

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Q: (v) er-y de +e**"dy = o

A: We will solve the differential equation by the method of separation of variables.

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: d, 3 Find dx -)- + x(х - 1)). A -3 +2х-1 B +1 -3 +1 -6 +2х-1 x3 (D

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Q: [d] If xz = yz and z - 0 then x = y

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Q: ysina dady.d.z. 2.

A: we have to calculate  ∫0π6∫01∫-23ysinzdxdydz ∫0π6∫01∫-23ysinzdxdydz=∫0π6∫01∫-23ysinzdxdydz…

Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: Homogenous DE (D^3+5D^2+D)^2y=0  y(0)=3, y'(0)=2, y''(0)=8

A: The given differential equation is: D3+5D2+D2y=0 ;                        y(0)=3,  y'(0)=2,…

Q: L[(t + 1)2e] = ? %3D s2-1 s2 +1 (s-1)2 (s – 1)2 -

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Q: Find dy. y = x| 13 dy = (Simplify your ans × |5

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Q: dy (B) Find -, if dx 3x2 + 2x 2 Y = (- when x = 1 5

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Q: Q.2 JJR ex2-2 dxdy, where R between x2 =-y, y = 0 and x = -3 , y = -9

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Q: dy Q. 8 Find 2 -: if Y dx 6x4+1 -48x3 (6x4+1)² .4 -48x (6x4+1)? -84x3 (6x4+1)? None

A: Given that  y=26x4+1

Q: B2. Evaluate (x? V1+x dx by using substitution method.

A: Integration

Q: 13. f(x, y) = x³ – y³ – 2xy + 6 %3D

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Q: 8. Find when x = t3 -t and y = 4 –- t². dx'

A: Here, the given functions are: x=t3-t & y=4-t2⇒x'(t)=ddt(t3-t)=ddt(t3)-ddt(t)=3t2-1…

Q: -6 Let y = ( 5x + . Then dy - A(5x + )" (5 -)". = A 5x + where %3D B = C = D =

A: To find the derivative of y with respect to x

Q: 33. f(x, y) = xr – 3xy² + 6y²

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Q: 3 Evaluate 2z (4 – a – y) dy dæ.

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Q: 1.y =z+1

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Q: dx is is equal to: 2x/4-(2x)2

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Q: Q3: if f(x)= xy+2x-5y =2 then dy/dx3D a- b- C-

A: We know that dy/dx mean difernciate f(x) with x. From this we will get our answer.

Q: d²y 15. If y3 - xy = 5 , then dx2 -2xy В. (3y2-x)3 2xy А. (3y2-x)3 2xy С. (3y2-x)2 D. (3y²-2x)3

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Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

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Q: Q2:Fid for : y = ncothx + sechx* dx

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

Q: 7. y Vzy dz + dy = 0

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Q: + 2e* – 4V¤)dx , where f(0) = 7 -

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Q: and Y=-2 when X=Z dx

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Q: • ["* [*, [° 42²y — 2²³ dz dy dz J1 1. Evaluate

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answers of rest,…

Q: 8.) Find of y3 = x* + 3x d?y dx2

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Q: Calculate ∂ω/∂x for ω=ze(xy^2+2z) Do not include "∂ω/∂x=" in your answer.

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Q: Q2: Find for (x+y) +(x- y) x +y* %3D dx

A: Derivative wrt x

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: dx What is the best substitution to evaluate V2x 2х - х* |

A: Given I=∫dx2x-x2If we consider x=1+sinθ and dx=cosθdθthen,I=∫dx2x-x2=∫cosdθ2(1+sinθ)-(1+sinθ)2

Q: 3 Evaluate: (4x²yz - z dz dy dx 24

A: The integration of the triple integral is (4x2yz-z4/4), z from 0 to 1, y from -1 to 4, x from 2 to…

Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: 2. Find in terms of Jo and J,: x²½(x)dx

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Q: Find the antiderivate of dx/(x2+4)3/2

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Q: どa (en) (2-x)8 y = X+7 FiNo dy

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Q: 5. If x-2ry+ 3y² = 8, then dx %3D 8+ 2y -2x (A) 6y-2x Зу - х (В) y-x (C) 113

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

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Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: 18.t2y′′−4ty′+6y=0,t>0;y1(t)=t2

A: