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Question: 5 12 points equations of the form are called bernoulli...

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5. (12 points) Equations of the form are called Bernoulli equations. Use the substitution w-yl-n (with appropriately chosen n) to reduce the problem to a linear problem and find the solution. 6. (a) (6 points) There is another way to solve Bernoulli equations. First, notice that it is easy to solve the equation y + p(x)y(x)-0. Its both linear and separable. Say that yı is a solution of this equation. In other words Now substitute y(x) - u(x)y/i(x) into equation (1) and use equation (2) to get a simple equation for the unknown function u. What resulting differential equation do you get for u? You should be able to see that this equation is separable. (b) (6 points) Apply this method to the problem from Question 5. Find yi, u, and the solution y. Compare to the solution you found in Question 5 to ensure that they are the same.

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