Posted by **ryan j** on Wednesday, October 26, 2011 at 9:45am.

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.

- maths -
**Steve**, Wednesday, October 26, 2011 at 5:49pm
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}

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