Let y = y(x) be the solution to the initial value problem dy ezty. dx y(0) = -1. Find the value of y(1). O DO NOT EXIST O In(e+1) O In(e+1)

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Q: dy 2 %3D

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Q: 1. Find the particular solution for the initial condition y(0) = 2 for the equation e yy' + x = 0.

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Q: 3. Find the solution of the given initial value problem. dy y = xe", y(1) = e – 1, x > 1 | dx

A: I am attaching the solution of question (3) only.  The solution is, y = x(ex - 1)  The detailed…

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A: NOTE: Due to time limit answer of 1. is given here, for others please ask in a different question.

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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.