Solve the following ordinary differential equation by the method of separation o

Question

Solve the following ordinary differential equation by the method of separation of variables. dz / dt = -2(5-z3) / tz2) when z(1) = 0 Recall that some differential equations can be written in the form q(z) z = p(t) When this happens then one can write int q(z) dz = int p(t) dt + C and have an implicit solution. In some cases this the implicit solution can be arranged to find an explicit solution z(t). What is the explicit solution of the given differential equation? Enter just an equation of the form z = (some expression in t only).

Explanation / Answer

z = 3t^3 - 2t^3/2 + 63

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