Homework Help: maths

Posted by Zane on Wednesday, October 26, 2011 at 9:22am.

find the general solution of the following first order differential equation.

u(t): du/dt = u /t+2t

pls show all working

differential equations - drwls, Wednesday, October 26, 2011 at 10:18am
I assume you mean
du/dt = (u/t) + 2t and not
u/(t + 2t) = u/(3t)

Your D.E. is of the form
du/dt + Pu = Q
where P = -1/t and Q = 2t

The method of "integrating factors" can be used. Your textbook should have an explanation of the method.

There is a function rho(t) given by
rho(t) = exp(integral of P(t)dt)

such that the solution is
rho(t)*u
= integral of (rho*Q) + C

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