maths
posted by ryan j on .
help find the general solution of the following first order differential equation.
t*(dy/dt) = (y/t) + ((exp(1/t)/t^3)
could you show steps in working to sol.

I like x instead of t. You have
xy' = y/x + e^(1/x) / x^3
Change to the form
y' + yP(x) = Q(x)
y' + y*1/x^{2} = e^{1/x}/x^{4}
Now find the integrating factor
IF = exp(Int(P(x)) = exp(Int(1/x^{2})) = e^{1/x}
Now, y = 1/e^{1/x} Int(Q(x)*IF)
= e^{1/x} Int(e^{1/x}/x^{4} * e^{1/x} dx)
= e^{1/x}*(1/3x^{3} + C)
y = Ce^{1/x}  e^{1/x}/3x^{3}