Suppose that a fourth order differential equation has a solution y=−8e5xx cos(x). Find the initial conditions that this solution satisfies. y(0) =   y′(0) =   y′′(0) =   y′′′(0) =

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A: Solution:

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A: Given solution of a certain differential equation is,

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A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

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A: One distinguishes the following cases: Point a is an ordinary point when functions p1(x) and p0(x)…

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A: To solve the following problem

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Q: determine the general solution to thegiven differential equation. y′′′ − y′′ + y′ − y = 0.

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A: we  have to find the solution y(t)  by using initial condition. The solution of differential…

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A: Given :

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A:

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

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Q: x²y" - xy'+ 5y = 0

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A: y''-2y'+y=4x2+ex This has characteristic equation               λ2-2λ+1=0λ-12=0λ=1…

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A: To find The general solution of the ordinary differential equation.

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A:

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Q: 1. x²y y' = ey

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Q: Find the general solution of the given higher-order differential equation. y" - 2y" - 3y' = 0 y(x) =

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Q: dy dx 11 - 4xy, when x = 0, y = 2

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Q: If y=3 when x=0 and y'=4 when x=0, determine the particular solution of this initial conditions,…

A: The given differential equation is                                                   y''-2y'-3y=0…

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.