Q2/ Consider the Fredholm integral equation of the second kind, 1 y(x) = x – | xt y(t)dt by using successive approximations method prove that 3 y(x) = %3D

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

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Q: 7. Evaluate using integration by parts: f Væ log, x dx.

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Q: У (2ху + 1)dx — хӑу %3D 0 ||

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Q: (x + y) dx dy Jo Jy/2

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is…

A: Given query is to rewrite the integrand in integrable manner.

Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dy is given by - 5x + 9y = x5…

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Q: HiW 4i Solve the Pollowing Integral dy y-zy-3 16x3 dx 4火 -4X +1

A: According to our guideline we can answer only one question and rest can be reposted.

Q: Evaluate the integral. (Use C for the constant of integration.) dt 1- t10

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Q: Q2:A/ Evaluate the integrals 1 sec²(eVx + 1) dx J Vxe-V

A: Given: ∫1xe-xsec2ex+1dx Consider, u=ex+1, du=ddxex+1=ex+1ddxx+1=ex+12xdx

Q: Q2/ Evaluate the integral: 6. xe' dy dx by changing the order of integration.

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Q: Evaluate the integral r4 pr=/2)+1 2x –- y -dx dy 2 o Jx=y/2 from Example 1 directly by integration…

A: Given,         ∫04∫x=y2x=y2+12x-y2dxdy=?

Q: 1) Find dy/dt for if : y = log2 (8r'n 2) %3D 2) Evaluate the following integral: In 2 ` log2 (x +…

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Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 1. Evalute the improper integral 3x dx. J ' 1+ x² -1

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

Q: 1. Evaluate the given double integral by first changing its order of integration 1 •1-y² ye(1-x)² dx…

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Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

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Q: Evaluate the integral. (Use C for the constant of integration.) t3 In(t) dt C must be in capital…

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Q: Construct Green's function for the differential equation xy" + y = 0, 0<x<l under the condition that…

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Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: When approximating f(x) dx using Romberg integration, R4,4 gives an approximation of order:

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Q: 18x? Evaluate the integral: -dx V49 – x2 -

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Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

A: The given integral is ∫02∫x22ey2dy dx In original integration, the integration order is dy dx. Our…

Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: Find the integral. (Use C for the constant of integration.) [(++ 3)cos( 2 + 6t) at (t + 3)cos( t2…

A: To find the integral

Q: 6. f(x)dz = f(t)dt, If what are the bounds of integration for the first integral? = and b =

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Q: Q1/Evaluate the integral: -За (2Vах dy dx x2 0, 4a by changing the order of integration.

A: We have to solve given problem:

Q: Q3: Reduce the integral Sx³J2(x) dx to integration in terms of Jo(x)

A: To find - Reduce the integral ∫x3J2x dx to integration in terms of J0x.       Formula used - Bessel…

Q: Consider solving the autonomous differential equation dy = f(y), te [to,T], y(to) = yo %3D dt with…

A: First we will define what is the meaning of error and then truncation error. Error means there is a…

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Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

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Q: da dt dy 1 Int x + dt

A: Given Differential Equations are                                                         dxdt=y,…

Q: 2. u(x)= secx+à So u(t)dt.

A: Given integral Fredholm equation, ux=sec2x+λ∫01utdt To find the solution of this equation.

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A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: (i) Change the order of integration in the integral Vi-x dx dy (1+ev)NI-x²-y and hence evaluate.

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

Q: 3 In (sec v) 2t Evaluate the integral ex dx dt dv. 00

A: Topic = Integration

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Q: If the input x(t) and the output y(t) are connected by the differential equation dy(t) T + y(t) =…

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Q: Evaluate the integral: .0 ²/3 t ln u tan s ds du dt 2e π/3

A: Given: ∫-10∫e2e∫0π3t lnu tansdsdudt

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Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: o integrals are equivalent and (b) calculate 2. | sin(t) dt = sin(x + 1) dx %3!

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Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: Verify the function z(x,y)=Vx sin is a solution of the following partial differential equation…

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Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.