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Solving a Bernoulli Differential Equation In Exercises 57-64, solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form
that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is
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Chapter 6 Solutions
Calculus of a Single Variable
- EXERCISES Find the general solution for each differential equation. xdydxyx=0,x0arrow_forwardNewtons Law of Cooling Newtons law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if T is the temperature of the object after t hours and TM is the constant temperature of the surrounding medium, then dTdt=k(TTM) where k is a constant. Use this equation in Exercises 58-61. Show that the solution of this differential equation is T=Cekt+TM where C is a constant.arrow_forward
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