y' = y*. (a) Find an implicit expression for all solutions y of the differential equation above, in the form p(t, y) : = c, where c collects all integration constants. p(t, y) = t + (1/2)y^-2 Σ Note: Do not include the constnat c in your answer. (b) Find the explicit expression for a solution y1 of differential equation above that satisfies the initial condition Y1 (0) 1. Y1 (t) = sqrt(1/(1-2t)) Σ (c) Find the largest value tį such that the solution y, is defined on [0, t1). t1 1/2 Σ

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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.