Solve the given Volterra integral equation by resolvent Kernel method (see it is a difference Kernal) u(x) = 29 + 6x + | (5– 6(x – t))u(t)dt

Q: The Euler method for approximating a solution to the first order IVP: y' = 3x + 5y, y(1) = 7 with h…

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

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

A: We have to find out the operation

Q: Vhat is the integrating factor needed to solve for the general solution of the given differential…

A: Use integrating factor formula

Q: calculate the integral of: e(x^2/2)

A: We'll use the Maclaurin series expansion for e^(x^2/2).

Q: (2ах + b)А + В dx. The form of decomposing a single irreducible quadratic factor in agiven integral…

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Q: (x – x² – y²)dx + (y + x² + y²)dy = 0

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Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dx2 dy -3x +4y =x5 is given…

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Q: 3. S "(o2-1)dv v2+1

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Q: 15x²x³43x - 19 The integral f S can be rewritten as (x + 1)²(x² - 6x + 13) Ax + B C D Slax + + ax² +…

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Q: Exercise 2. Find the general integral of 1" - (2+a)r' + 2ax – 4 = 0 in dependence of a € R, a # 2.…

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Q: e3t dt 2 (1+4e*)

A: Please refer the attached image for complete solution.

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: (2х — Зу + 1)dх — (3х + 2у — 4)dy %3D 0

A: To solve the given first order differential equation.

Q: 1 Solve the integral equation S f(x – t)e-at dt - f(x) using Fourier transform x² + b² -00 to find…

A: Definition of Fourier Transform : Let f(t) be defined for all t∈(-∞,∞).Then the fourier…

Q: 10. What is the constant multiplier to complete the integrand in terms of u for dx? x +3 A) B) C) 4…

A: 10. The given integrand ∫x3x4+3dx11. The following integral is equal to 54.

Q: Use the method of variation of parameters to find the complete solution of the following…

A: we have given d2ydx2+y=xsinxfirst we find C.Fm2+1=0m=±iy(x)=c1cosx+c2sinxu1=cosx,u2=sinxnow find…

Q: Consider V /3x² + 3y²dxdy The integral cannot be solved analytically using basic integration…

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: Consider the IVP y'=sin° y +1 for y(0) = 0. (a) Use Euler's method to approximate the solution for…

A: Given the equation y'=sin3(y)+1, y(0)=0

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: e the method of u-substitution to evaluate the given integrals. 4t dt 2 – 8t2

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Q: 3t e2t dt Evaluate the following integrals. 4 Зе + - 5t5/2 a dt - t3 2x cos(9 - x2) dx sin(9 – 2) -…

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Q: Use Euler's method to compute an approximation X(0.65) to the solution x(0.65) of the initial value…

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Q: Find the general solution of the following DE by finding an integrating factor to maket eact Hint:…

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Q: 11) Evaluate the iterated integral 3 3 -8y2 dydx. Switch the order of integration if necessary.

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Q: 15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t…

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Q: 1 (a) Solve the following Integral equation using Adomian Decomposition method e-(x+1) _ + 1 u(x) :…

A: Here given the integral equation

Q: cos(x + y), when x = 0,y = dx

A: To solve the given first order differential equation using integration method. dydx=cos(x+y)  , when…

Q: Solve the differential equation by Frobenius method with coefficients represented up to and…

A: Solution :-

Q: Suppose g(z) zn 2nn n=1 Σ Solve for the value of the integral 1 2-₁ / e²g² (2) dz 2πi |2|=1 using…

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Q: 5x dx. - 6 Compute the integral x2

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Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

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Q: 6.3.18. Evaluate the integral. using U substitution integrate (cos^2(x)sin^2(x))dx

A: Hello, there are two functions present in the question. As the first function comes along with the…

Q: (2x+5)² 2. What should be the rewrite of the integrand of ſ x2 dx so that the resulting integral is…

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Q: Example 6. For what value of A, the function g(x) = 1 + 1x is a %3D solution of the integral…

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Q: Solve the Abel's integral equation: a dt = æ(1+x) y(t) (1-t)1/3

A: Given integral equation, ∫0xyt1-t13dt=x1+x

Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: The differential operator (D2 - 16D+113)³ annihilates the functions

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Q: 13. Identify the best integration technique for the following: (sin.x cos³x) dx A. Partial Fraction…

A: Identify the integration technique

Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

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Q: 25 2 8 5 cos (x²) 4Vz Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Consider the provided question, We have to find the integral ∫025∫02∫4y85cosx24zdxdydz by changing…

Q: Consider the indefinite integral Ва3 + 21? + 5а + 0 dx x² – 1 | Then the integrand decomposes into…

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Q: (a) Find a second-order homogeneous linear ODE for which the given functions are solutions. (b) Show…

A: Given,  (a) Find a second-order homogeneous linear ODE for which the given functions are solutions.…

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Solve the initial-boundary value problem Utt = 16uzz u (0, ) u(π, t) 0 u(x,0) = E sin(nx) u:(x,0) =…

A: ∂2u∂t2=16∂2u∂x2u=XT . . . . (1) Where X and T are function of x and t. ⇒∂u∂t=XdTdt,…

Q: (3) Using Hilbert-Schmidt theorem, solve the following integral equation: (1) y(=) = (x+2)*+ /…

A: Given integral equation, yx=x+22+∫-11xt+x2t2ytdt          ...1 Here fx=x+22, λ=1 Firstly find the…

Q: 4.3 Can you show me the steps to solve 29?

A: Given the integral,

Q: a2u 2) дхду ди 6xe* (factor integración) ду - %3D

A: