3. Bernoulli differential equations Given two functions pix} and 9(1), an equation of the form if}? + air)? = air)?" in 9'5 D11} is called a Bernoulli differential equation. {a} Stare at this equation for a few minutes and convince yourself that it cannot be solved directly using the separation of variables or integrating factor methods. (No need to write anything this is purely a thought exercise.) {b} Show that by multiplying both sides of the equation by the factor [1 rib'1 and then dening a newsr function zix] = y{x}l_", you reach an equation for 3(1) that can be solved. From this, derive a formula for the solution x), expressing it in terms of the \"input" functions pix} and 13(1). {c} Explain why the population growth equation from Problem #4 in section 2.4 in the textbook (page 33} is a special case of this family of differential equations