Question

(1)Find the equation of the tangent line to the hyperbola at the given point:

x^2/a^2?y^2/b^2=1 (m,n)

and write your answer in the form y=f(x) for some function f(x) . Enter f(x) in the box below.

y=

Note: your answer should be in terms of x,m,n,a, and b .

(2)) Verify that every member of the family of functions y=(lnx+Cx)/x is a solution of the differential equation x^2y?+x^y=1. Answer the following questions.

1. Find a solution of the differential equation that satisfies the initial condition y(3)=10.
Answer: y=

2. Find a solution of the differential equation that satisfies the initial condition y(10)=3.