Exer 1. Solve the following first-order boundary value problem 2 u +4 u, + 40 u = u(z, 0) = e* 60 e+2v + cos(8 z) e. DDE with no

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

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Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

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Q: , 0 0 u(0,1) — 0, и(п,г) %3D0 sinx, u (х,0) — 0 Utt = Uxx, u(х,0) 3D

A: Consider the solution: ux, t=XxTt and the conditions are X0=0=Xπ, T0=fx=sinx and T'(0)=0  uxxx,…

Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

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Q: 3 1 Evaluate the iterated integral 12x -1 0 3 1 °dy dx = -1 0

A: Evaluate the iterated integral.       ∫-13∫0112x2y3dy dx

Q: 5. Find two solutions (not multiples of each other) of the Bessel equation of order x*y" +xy' + (x²…

A: The general form of the Bessel equation is ,                                          x2y" +xy'…

Q: SVEsin(1+ VF )dz 4 Vz sin .3

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Q: In 3 xp; J(1-x)*dx

A: Given,

Q: Let C be the shortest path that connects z to mi and /= . (sinhz + 1)dz. Then |=-1-cosh t+ n(1-1)…

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Q: Assume that after months, butterflies’ populace in 1000 is calculated as: f(w) = 12w + cos(16w)…

A: Given f(w) = 12w + cos(16w) +n * 100

Q: 2z+1 37 Prove the equation through integral calculatipns. dz < 5+z? 2

A: We will do the proof step by step.

Q: dx 1 = [- 1+vx+1

A: To evaluate: I=∫dx1+x+1

Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: (a) Solve the initial boundary value problem by separation of variables : Utt = 4u7z 0 0, u(0, t) =…

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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: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: Find a general solution of each reducible second-order differ- ential equation y" = 2y(y')3

A: Given the differential equation:

Q: Find a general solution of each reducible second-order differ- ential equation yy" + (y')² = 0

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Q: Find a general solution of each reducible second-order differ- ential equation y" = 2yy'

A: Recall the chain rule of calculus:

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: 1. Evaluate the integral 2 1-2 8x cos y dy dr y - 4 by reversing the order of integration.

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Q: 2/3–2 dx integralinin değeri x² + 4x + 8 aşağıdakilerden hangisidir?

A: The integral can be solved using completing the squares method. Since the integration is definite…

Q: (a) Evalate the integral||xydy dx. 12

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Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

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Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

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Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A: The volume of the spherical balloon is ,

Q: 3. Find the residues of the functions 1- cosz а.) b.) c.) z'e at z=0; .5 e -1 and express the types…

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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: Compute the first-order central difference approximations ofO(h^4) of t function of y at x = 1h =…

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Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: Solve the line integral if path A is a0- (-2+2i) Al= 0+2i A2= 0-2i A3 - 2-2i (3+ 2 )' dz A

A: In mathematics, a line integral is an integral where the function to be integrated is evaluated…

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.

Q: Determine the largest interval (a, b) for which Theorem 1 from section 6.1 guarantees a u solution…

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Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (y')2

A: Given, The differential equation y"=(y')2 .               ................(1)

Q: Show that this function satisfies the initial conditions y,(to) =0 and y'(to) = 0, so it is a…

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Q: Compute the following Gaussian integrals. 1. xte-aa2 dx 8. 2. xe-ax dr

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

A: Let's find.

Q: Find the partial integral. (3х + 5y) dx

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Q: In 3 In 2 5. exty dy dx

A: ∫0ln 3∫0ln 2 ex+y dy dx First integrate inner integral        ⇒∫02 ex+y dy=∫0ln 2ex·ey dy=ex…

Q: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0

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Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3 y = tan x

A: In this question, we find the particular solution of the differential equation. Here, we used the…

Q: Find a general solution of each reducible second-order differ- ential equation y" + 4y = 0

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Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these O…

A: Evaluate this integral from initial to final point.

Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3y = tan x

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Q: state where in the ty-plane the hypotheses of Theorem are satisfied 6. y′=ln|ty|1−t2+y2

A: A hyperbola is an open curve with two branches, which are symmetric and are mirror images of each…