(a) What can you say about a solution of the equation y' = -y2 just by looking at the differential equation?(b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a).(c) Can you think of a solution of the differential equation y' = -y2 that is not a member of the family in part (b)?(d) Find a solution of the initial-value problemy' = -y2                    y(0) = 0.5

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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.