H. Convert the following Volterra integral equations to an equivalent initial value problem (IVP). (x-t)²u(t)dt u(x) = x³. +

Q: Hw.1. Solve the integral equation g(s) = f(s) + a S,(s + t) g(t)dt

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Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: Conduction equation Solve the heat Uxx = Ut -U; U = u(x, t)

A: uxx=ut-u

Q: In 2 I = t-2 e(-1/t) dt

A:

Q: dP Pt, P(1) = 3 %3D dt

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Q: Solve the following DE: y" = 3[(y)² + 1]

A: Differential equation

Q: 4. Solve the following DE: (2x²y)y' = x³ + 2y³

A: Given in the question, The diffrential equation is as follows:- By dividing both sides by 2x2 * y3,…

Q: Calculate (1/2 (2 (2t - 1)e³t dt.

A: Integrate ∫0122t-1e3tdt

Q: Consider a pond that initially contains 10 million gal of fresh water. Water containing an…

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Q: dx + 2– + x = u(1) x(0) = x'(0) = 1 dt

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Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

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Q: dT +kT =200k, where k is a constant. dt Solve A. T=ce" + 200 B.T= ce–200 C. T=ce +200 D. T= ce"+200e…

A: See the detailed solution below.

Q: A. Consider the First Order Linear Differential Equation in Standard Form dy / dt + p(t) y = g(t),…

A:

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: Ex.: Solve dx dy 2=t.... dt dt dx dy -+2 +2-y=0... y = 0.. dt dt

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Q: 5 +4y = 2 y(0)=1 dt

A: Given problem is:

Q: A(x) = sintdt d. A(x) = ₁ It-2|dt

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Q: 1- dt 2x 1 d Q10:- Calculate dt dx 2x 3- dx 'x SLn(t) dt. dx 'x

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Q: (b) Solve: (x*D² - 2XYDD' - 3y'D? +xD-3yD')z = x'ycos(Inx').

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Q: u(x, t) = ear+bt %3D 1 u(x, t) = -/at %3D

A: The given functions are ux,t=eax+bt and ux,t=1te-x2/at.

Q: Use Euler method to solve ODE; y' = 1 + x2 ; y(1)=-2 ; h=0.10 ; x(0)=2 to determine y (2.10),…

A: solution:           given that y1 = 1+n2 with y(1) = -2 and h = 0.10 , we haveto determine…

Q: 10. Evaluate the following: (a) (b) -3 dr (z+ VE) dz (c) (d) */4 sec? e de

A: