Fill in the blanks (1 point) A Bernoulli differential equation is one of the form dy…

Fill in the blanks
(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy” (*) dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du dac + (1 – n)P(x)u= (1 – nQ(2). Consider the initial value problem xy’ +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form (*) with P(2) Q(x) = and n= will transform it into the linear equation (b) The substitution u du dc U= (C) Using the substitution in part (b), we rewrite the initial condition in terms of x and u. u(1) (d) Now solve the linear equation in part (b). and find the solution that satisfies the initial condition in part (C). u(2) = (e) Finally, solve for y y(2) =