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Suppose y(t) is governed by ODE t3y'''(t) + 6t2y''(t) + 4ty'(t) = 0. Solve this ODE...

Suppose y(t) is governed by ODE t3y'''(t) + 6t2y''(t) + 4ty'(t) = 0. Solve this ODE by performing the following procedure: 1) Let x = ln(t) and set y(t) = φ(x) = φ(ln(t)), 2) Use chain rule of differentiation to calculate derivatives y in terms derivatives of φ, 3) by appropriate substitution, construct an ODE governing φ(x) and solve it, 4) use this φ(x) to get back y(t).

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