AssIGN MENT2 : 2nel Order Homagenats ODE Egu 8 Fid geresal selution for ;- =0 | dx² dx y" -12 g' tlly=O ylo) =3 y')=1/ gren

Q: find dy /dx for Hhe followin FanX +Sin y %3D

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Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)

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Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: 20 dv on the interval [0, 20] dt du dt 20

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Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A: We need to evaluate the integral ∫C(8x+12ydx+(9x-y)dy along the parabolic arc y=x2. from (0,0) to…

Q: Sev dx (Hint: Integrate by parts with u-substitution)

A: To evaluate I=∫exdx

Q: dy Let ry = 1 and dt 5. dx when x = 5. dt Find

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Q: The vahe of the integral fx*dx with step length 0.5 using Trapezoidal's nule is a) 0.375 b) 0.875 c)…

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Q: Evaluate the integral / (4x + 18y) dx + (27x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

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Q: Differentiate: y = /16 – z² – 4 arccos() e+4 y' = Oy= Oy- %3D

A: Given that : y = √(16 - x2) - 4arccos(x/4). We find derivative of this function (y).       Here i…

Q: Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the…

A: Solution: Given the Sine-Gordon equation utt-uxx+sinu=0   - - - - - (1) and initially conditions;…

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Evaluate the double integral : 9. dy dx 0, 22

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Q: Evaluate the integral | (6x + 3y)dx + (9x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

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Q: Find the Particuldr int egral Por the giren egh giren eqn dzy + 16y -4X + COS4X ニ

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Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

Q: is the follecing dif Mantial opuatíon Jmeo on mot Y with x>1. ey-x

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Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: e following integral: 23 8xyz dz dx dy. 120

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Q: the double integral dy dx Evaluate 2.

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Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

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Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

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Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: dz Different iate implicit ly to find and if z'yz + In(ry) + sin(yz) = 10. ду

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Q: DIfterenti are (뉴) de Ipx tan x -In DIfterentiate exy te Yy 1, tnd y"

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

Q: Assume that y=5x and dx/dt = 8 find dy/dt

A: Differentiate by chain rule : →f(g(x))dx = d(f(x))d(g(x))×d(g(x))dx.

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: Evaluate the integral (4x +9y)dx + (9x – y)dy along the parabolic arc y = r from (0,0) to (1,1). (4x…

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Evaluate the integral | (2x + 9y)dx + (21x – y)dy along the parabolic arc y = x from (0,0) to (1,…

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Q: Find dy/dt. show all work y=cos(square root of 8t+12)

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Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

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Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.