When do the following integral equations have solutions? 3. u(z) = f(x) + A S u(t)dt.

Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

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Q: dx = cx – bx? dt

A: Variable separable method

Q: u(x) = +2x sinh(z/4)− x |, etan''u(t)dt.

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: Evaluate L¹ (75+5=3]}] -(5+2)

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Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: J 5(x) =-J5(x) ylgn O İhi O

A: We have to solve given problem:

Q: Calculate and plot the potential V(x), up to an arbitrary constant, for the ODE d x(t) = =-X.

A: To calculate the potential V(x), we integrate the given ordinary differential equation (ODE) with…

Q: F(x) = sin t dt, [0,1] 0. F(x)]

A: The following formula for Maclaurin's series expansion of sin x will be used: sin x=x-x33!+x55!-...…

Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 4.…

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Q: Determine which of the differentials (or both) is the total differential: a) 2[cos(2x+2y²) + x ] dx…

A: a) 2[cos(2x + 2y²)+x] dx - [4y sin(2x + 2y²) + 1] dy is not a total differential, because it is…

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 4, assuming that a(4) =…

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Q: Using this part of the Fundamental Theorem of Calculus: :| f(1) dt = f(x) a find (5c4 — Зс + 7) dc.…

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Q: Let G(x) = ²* w(t) - [² d dt. t4 a Find a function, w, and a number, a, such that G(x) = 4x¯ w(x) =…

A: Given G(x)=∫axw(t)t4dt and G(x)=4x-2-1

Q: FTnd the General/Practical solution FoT +he Following DTFFerentiat equation. {x-9x? + 16x - 144)y?dy…

A: The differential equation is given as x3-9x2+16x-144y2dy=2x2-1e4ydx find the general solution.

Q: Solve the Schlömilch's integral equation 4. u(r sin t) dt, -T SIST. 1+x =

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Q: L+ Ri = E,where L, R, and E are constants when t = 0,i = 0 dt %3D

A: We have to find the solution of  given first order linear differential equation

Q: 1. Use the "First Fundamental Theorem Of Calculus" to find the first derivative of the function. 2 –…

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Q: Solve for x: X S₂ 14 2 1 t(4- t) dt= 0.5, where x € (2, 4).

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Q: Q4. Using Fourier Transforms, solve the following Integral Equation for f(t): f(l) - ff(t-u)ue ²2 H…

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: dx Assume that x= x(t) and y = y(t). Let y = x³ +5 and dt=4 when x = 1. Find dt 11 dy when x = 1.…

A: The objective of the question is to find the rate of change of y with respect to time (dy/dt) when x…

Q: a). Sketch the slope field of the differential equation. (x - y); within the Interval -3 ≤ x ≤ 3 -3…

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Q: Classify the following differential equation: e* + 3y = x²y dx a) Separable and homogeneous b)…

A: Solved below

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.