dY Given the initial value problem :) ),¥0) = (?) whose matrix has a repeated %3D dt eigenvalue A - 2, find the general solution in terms of the initial conditions. %3D 2(t) Write your solution in component form where Y(t) = ). Your answers should have the variables p %3D and q in them. Enter an answer like (2p - g)te- as (2p-q)*te^(-3t). Please note the * in this expression! Be sure to PREVIEW your answers before submitting! x(t) = %3D 2(t) Preview:

Q: 2. Solve the differential equation: a. y' = xe-sinx – y cos x

A: We will solve the problem

Q: 1. Consider the differential equation (which we saw on the wk 1 test) dy %3D У (у + 1)?(2 —у) dt…

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Q: What is the degree of homogeneous differential equation (x+y)dx + x² + y² dy? А. 1 В.2 С.3 D. 0

A: Given differential equation is of the form       M(x,y)dx+N(x,y)dy   So we assume…

Q: Find the general solution to a?y" + 5xy' - 2y = 0. OA. y = cje 4x + cze OB. y = c1x4 + c2x1 OC. y =…

A: Given differential equation is x2y''+5xy'−2y=0....1 The given differentia equation is in the form of…

Q: Subject: Differential Equations y" – 3y' + 2y = 2x? (D2 – 5D + 4)y = 4x 1. 2.

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Q: y= Ae* + Bxex

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Q: 2+ ye*y y' = 2y – xe*y ху %3D

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Q: Differential Equations   Use Euler's Method to solve the differential equation: dy/dy=5⋅y+4⋅t…

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Q: “些。 de e +1 dr

A: Here we will use separation of variable method.

Q: nat is the degree of homogeneous differential equation below? + y?)dx+ xydy = 0? %3D 1 3

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Q: 3) * + 4x = 4(sec 2t)²

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Q: dy √1-y² dx Hint: Separation of variables

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Q: (D3-D²)y =0

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Q: Laplace transform is a process wherein a function of "t" be converted to variable "_

A: Using the definition of Laplace transform

Q: F(s) means Your answer

A: Using the definition of Laplace transform.

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: (D³ + 1)y = xe2x 1.

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Q: (x+y) dx = (²x y J J y so

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Q: cy² = x² + y

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Q: Solve en

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Q: ck. 3 use the annihilator method to solve the differential equation y" + 6y² + 8y = e³x - sinx

A: (.) given differential equation is,        (.) General solution is given by,                  where…

Q: Compute L-{-6s+13 с.

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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.