I have the following two questions to solve(adsbygoogle = window.adsbygoogle || []).push({});

Problem 1.

3x' + 1/t x = t

and

Problem 2.

x' + 1/t x = ln t

I have followed a method detailed in my textbook to try and get an answer for Problem 1 but am a bit unsure so if anyone can clarify my workings below before I spend time trying to solve Problem 2.

3x' + 1/t x = t

Fits the format dx/dt + g(t)x = f(t)

For the integrating factor I(t) = e^∫g(t) dt

∫1/t = ln t

e^ln t = t

Multiply both sides by I(t) so the equation becomes d/dt(I(t)x(t)) = I(t)f(t)

3 d/dt (tx) = t^2

Then I(t)x(t) = ∫I(t)f(t) dt + C

3tx = ∫t^2 dt + C

3tx = (t^3)/3 + C

x(t) = ((t^3)/3 + C)/3t

x(t) = 1/6t^2 + C1/3t^-1

Does this look right? If so I will attempt Problem 2. Thanks for any assistance.

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# Homework Help: Finding the general solution of a first order diff eq with a variable coefficient

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