Q2. Consider the initial value problem (IVP) 2ydy – (2x + 1)dx 0, y(-2) = –1. a). Establish the existence and uniqueness of solution by stating the region.

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Here we are given a 1st order initial value problem. i,e y'=f(t,y) ,0≤t≤3 ,y(0)=y0

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A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

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A: Given problem is :

Q: O DE Linitial condelim) dy -48-7x y)= 1 +2

A: we have to find the diifferential equation dydx=4x2-7x3y2+2    with initial condition y(1)=1

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