Find the Laplace transform of the following differential equation and express it as a single fraction: + 2d + 16x(t) = 10e 8t where r(0) = 4 and z' (0) = 4 X(s) =

Q: у" — Зу' + 2у %3D2е3t y(0) 3D 0 у'(0) — 4 |-

A: Given differential equation is  y''-3y'+2y=2e3t given condition is  y(0)=0 ,y'(0)=4

Q: I want X(s)=

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Q: 2. L{ 2y" + y' – 5y = e“ }; when y(0) = 2, y'(0) = 1 %3D

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Q: Show that the transformation z = log tan (x/2) reduces the differential equation d²y +cotr +4x…

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Q: The differential equation is as follows: d[RL] -[RL]k2 dt with initial conditions, [RL], = [RL];=0…

A: So, we will have to use [ RL ]0  as a value in here, and hence, it will be treated as a constant.…

Q: Find the formula for the Laplace transform of the derivative of a function y'. Use the initial…

A: The solution is given as follows

Q: Consider the initial value problem I' + 3r = 45t, r(0) = 2. a. Take the Laplace transform of both…

A: Given differential equation is x' +3x =45 t,   x0=2

Q: xux-yuy+y2u=y2x find the general solution

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Q: Solve the following Differential Equation using Laplace Transform. y' – 3y = e-5t y(0) = 6

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Q: ve the differential equation using Laplace Transform and Inverse Laplace transform y" - 4y' + 4y =…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an LRC…

A: The given equation isLd2qdt2+Rdqdt+1Cq=E(t) substitute the given values 1d2qdt2+20dqdt+10.005q=140…

Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

Q: Find the Laplace transform of the following differential equation and express it as a single…

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Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: C. Use Laplace transform to solve the following differential equations: d²i dt² di dt +1000-…

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Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

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Q: Consider the following initial-value problem. y' + y = t sin(t), y(0) = 0 Take the Laplace transform…

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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.