(4 points) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn (∗) Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x). Consider the initial value problem xy′+y=−6xy2, y(1)=−7. (a) This differential equation can be written in the form (∗) with P(x)= , Q(x)= , and n= . (b) The substitution u= will transform it into the linear equation dudx+ 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(x)= . (e) Finally, solve for y.