Consider the differential equation for the function y y' = y. (a) Find an implicit expression for all solutions y of the differential equation above, in the form (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. Yı (t) = | sqrt(1/(1-2t)) Σ (c) Find the largest value tį such that the solution y, is defined on 0, t1). ti = 1/2 Σ (d) Find the explicit expression for a solution y2 of differential equation above that satisfies the initial condition Y2(0) = 2. Y2(t) Σ (e) Find the largest value t, such that the solution y, is defined on 0, t2). to = Σ
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