show that the differential eqn x^2 * dy/dx -y = 2x^3*e^(-1/x)
is linear, and solve it using the integrating factor method.
I have no idea how to even get started on this problem, if someone could show me in a few steps it would really help me out. I have alot more of these to do.
Ok, suppose you have a differential equation of the form:
Let (1) be an auxiliary function then:
But note that:
Thus, by the FTC: check in (1) that
Thus we have by (1) that:
This is the general solution to the first order equation
So suppose you are given for example, then you should let above