On page 51 we showed that a one-parameter family of solutions of the first-order differential equation dy/dx = xy"2 is y = (x* + c) for c > 0. Each solution in this family is defined on (-∞, 0). The last statement is not true if we choos c to be negative. For c = -1, explain why y = is not a solution of the DE on the interval (-∞, ∞). Find an interval of definition I on which y = (x* – 1) is a solution - of the DE.

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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.