Pind the ualue of e is an integrating facko of ly-y')+xy'so

Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: Apply the method of integration by parts to (In=) In æ ) (--) e dx dv

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Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

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Q: SOLVE IT BY USING INTEGRABLE COMBINATIONS BY INTEGRATING FACTORS FOUND BY INSPECTION y(2x − y +…

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Q: Integral in REVERSE ORDER

A: Given that  I=∫08∫y32ex4dx dy Limits are given y=0 and y=8     x=y3y=x3  and x=2

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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

A: To evaluate I=∫exdx

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: te dt.

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Q: The dimensions of a closed rectangular box are measured as 93 cm, 66 cm, and 50 cm, respectively,…

A: Given,           The dimensions of a closed rectangular box are measured as 93 cm, 66 cm…

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: dv Integrate ду 1 partially with respect to y. II

A: To partially integrate the given function with respect to y, implies x will be treated as a constant

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: By exchanging the order of the integration, the evaluation of siny dydx y klea

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Q: Find the sdution of the. differential equation that Satisies the qven intal condition

A: We have to find solution of differential equation with given initial condition.Differential equation…

Q: What is the integrating factor of xy' + 6y = 3xy3?

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Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

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Q: .2 What is the reversed order of integration of 1 dxdy? a. II Vx* +1 dydx 0, O b. x4 +1 dydx 0, .8…

A: Topic:- application of integration

Q: Find the derivative y= 0 to x^4 integral of cos square root of t dt show all work

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Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: A manufacturer produces a triangular lamina with a standard base and height of 30 cm and 12 cm,…

A: we have been given the measurements of a triangle a base = 30 cm and a height =12 cm  area of the…

Q: 5. – 3t te dt

A: The given integral is: I=∫t e-3t dt

Q: Let u=sinx and the integrand will lead to integration by partial fraction

A: use substitution method for solving the  integral

Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Find the Integrating Factor of dy + 2ytanx = sinx dx

A: This is 1st Order Linear Differential Equation.

Q: In² xdx

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Q: Q₁) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

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Q: When is it beneficial to use the Jacobian to change variables in a double integral?

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Q: When is integrating using the tabular method useful?

A: When is integrating using the tabular method useful?

Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: Evaluate In (ax) dx using integration by parts

A: Follow the procedure given below and use simple intergation by parts.

Q: 1 J sec- ztan - zdz

A: Solve the following

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: Find the limits of integration in cylindrical

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Q: Find the particular integ rel of This differential etuatim. (40²+HD+= 2e +8x %3D

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Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: Given: y = (In x)* , find dy/dx.

A: Given, y=logxx take log both side logy=xloglogx now derivate both side…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: 1. Evaluate LL vsin(a*) dx dy by first changing the order of integration.

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Q: What is the (a). general solution to xydx-(x+2) dy=0? (b) integrate.

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Q: Find the limits of integration with respect to u and v

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Q: Find an integrating factor depending only on x that will make 2ye 5x* 3 sin y + 5xex + dx + (x cos y…

A: Given:            Let the differential equation is in form 3siny+5ye5x+2ye5xxdx+xcosy+e5xdy=0…

Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: sketch , EvValuate & reverse order af integration de dy

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Q: Can you explain the integration by parts here?

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Q: Find the integrating factor of (x² - y²)dx + (x² - 2xy)dy = 0

A: Given  (x2-y2)dx+(x2-2xy)dy=0