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/x2 = e1/x/x4
Now find the integrating factor
IF = exp(Int(P(x)) = exp(Int(1/x2)) = e-1/x
Now, y = 1/e-1/x Int(Q(x)*IF)
= e1/x Int(e1/x/x4 * e-1/x dx)
= e1/x*(-1/3x3 + C)
y = Ce1/x - e1/x/3x3