y = 1/(x2 + c)  is a one-parameter family of solutions of the first-order DE  y' + 2xy2 = 0.  Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(−3) =1/6   Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)         Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval notation.)

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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.