, solve the following Volterra integral equations by using the Ado- mian decomposition method: 3. u(x) = 1 - 2 + f* u(t)dt 6. u(x) = 1-x+ € √(x - t)u(t)dt 0

Q: Use field II to sketch the graphs of the solutions that satisfythe given initial conditions. a) y(0)…

A: To use the given field to sketch the graphs of the solutions that satisfy the given initial…

Q: Find the quadratic approximation of f at x = 0 f(x) = sin In (3x + 1) O A. Q(x) = 1 + 3x + 5x 9 B.…

A: The given function is: fx=sin ln3x+1 To find the quadratic approximation of f at x=0

Q: 3. Use undetermined coefficients method to find a particular solution of the non-homogeneous ODE y"…

A:

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: d Calculateri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then…

A:

Q: Solve the following Fredholm integral equations by using the successive substitutions method: 1.…

A:

Q: Classify each of the equations above as autonomous, separable, linear, homogeneous, exact,…

A: I am solving questions ( B I and J ) as per the guidelines we can solve max 3 sub part of a question…

Q: (b) Solve the following IE u(x) = f* (z + 1²) dz by "Adomian Decomposition" method.

A: Solution:

Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

Q: Proposition3 1. Hxn enen and yw odd then x+y ù odd ond xy enen. xy ü odd ù odd and h enen. 2.4 xi…

A:

Q: b)(i) Use the successive approximations method to solve the following Fredholm integral equation.…

A: we have given Fredhom integral equation   u(x)=x+sinx-∫0π2xtu(t)dtnow use successive approximations…

Q: d d Calculate ri(t) · r2(t)] and [r:(t) x r2(t)] first by differentiating dt dt the product directly…

A:

Q: ind the number h 10+ r r.10

A: We have to look forward for such types of questions that ask for non-negative integral solutions of…

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

A:

Q: Consider the problem of finding the number of integral solutions of the equation ₁+X2+X3+ *4 = 20…

A: (a) The equation can be rewritten as follows by adding the variables  y₁ = x₁ - 3, y₂ = x₂ - 1, y₃ =…

Q: Find one particular solution to the following second-order forced equation d²y + 2y = cos (√2t) dt²…

A:

Q: d d Calculate[ri(t) r₂(t)] and[r₁(t) × r₂(t)] first by differentiating dt the product directly and…

A:

Q: Solve the PDE of the first order и, — и, — 0, и(х,Зх) — 2? и (х, Зг) — Ur – = x

A: Given problem is :