# maths

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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 -

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

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