Question

1. Consider the following equation that occurs in the study of the fluid flows: dy/dt=4y-y^2 (1)...

1. Consider the following equation that occurs in the study of the fluid flows:

dy/dt=4y-y^2 (1)

Leibniz came up with a clever substitution that converts the above non-linear ordinary differ-ential equation (ODE) into a linear ODE.

(a) Use the change of variables (u=y−1), to obtain a linear ODE for the dependent variable u; i.e. obtain an equation with u as dependent variable and t and independent variable,completely eliminating y.

(b) Solve the linear ODE for u and then substitute for u to find the original unknown y as a function of t.

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