Consider the following differential equation: dy dr cy - y; > 0 and >...

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Consider the following differential equation: dy dr cy - σy³; € > 0 and σ > 0, (3) where e and o are constants. This type of equation is called the Bernoulli equation after Jakob Bernoulli. This occurs in the study of stability of fluid flow. i. Is the equation linear or non-linear? V= ii. Show that the substitution (change of variable) v = y 2 reduces the Bernoulli's equation to a linear equation. This method of solution was found by Leibniz in 1696. Clearly show all steps including all mathematical manipulations. iii. Using the above mentioned Leibniz method solve the linear equation and then using the substituting find the solution of y(r). Clearly show all steps. Box the final answer. Consider the following differential equation: dy dr cy - σy³; € > 0 and σ > 0, (3) where e and o are constants. This type of equation is called the Bernoulli equation after Jakob Bernoulli. This occurs in the study of stability of fluid flow. i. Is the equation linear or non-linear? V= ii. Show that the substitution (change of variable) v = y 2 reduces the Bernoulli's equation to a linear equation. This method of solution was found by Leibniz in 1696. Clearly show all steps including all mathematical manipulations. iii. Using the above mentioned Leibniz method solve the linear equation and then using the substituting find the solution of y(r). Clearly show all steps. Box the final answer.