Let y : R →R be the real-valued function defined on the real line, which is the solution of the initial value problem y = -ry + 1, y(0) = 2. Which statements are correct? a) The problem is not uniquely solvable. b) The solution y(x) contains an exponential function. c) lim y(x) = 1 d) lim y(z) = 0

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Q: satisfying

A: We will obtain the particular solution.

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A: We will find out the required solution.

Q: Verify that the indicated function y = Q(x) is an explicit solution of the given first-order…

A: Solution : when y=125-x2y'=-125-x22×-2xy'=2x25-x22y'=2xy2thus in terms of x,2xy2=dydx

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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.