The discussion revolves around solving a differential equation using the method of separation of variables. The specific equation is x^2 dy/dx = y - xy, accompanied by an initial condition of y(-1) = -1.
Some participants have provided hints regarding algebraic simplifications and the properties of exponential functions. There is an ongoing exploration of how to derive the book's answer from the participant's initial solution, with no explicit consensus reached yet.
Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. The initial condition is a critical aspect of the problem being discussed.
[itex]\displaystyle e^{-1/x-\ln(x)+C}=e^{-1/x}e^{-\ln|x|}e^C[/itex]bdh2991 said:Homework Statement
use separation of variables to solve the differential equation x^2dy/dx=y-xy
with the initial condition of y(-1)=-1
The Attempt at a Solution
after i separated and integrated i got the answer y=e^(-1/x-lnx+c)
the answer in the book is y=e^-(1+1/x)/x
i can't figure out how they got to that even after i plugged in -1 for x and y
some help would be greatly appreciated
bdh2991 said:well i think it would be x^-1 so then that would give me the x in the denominator then plugging in the initial values i should get c=1?