Linear differential equation hwk check

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Ashley1nOnly
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Handwritten derivation in red marker on a whiteboard: substitution u = y^(3/2) turning y^(1/2) y' + t y^(3/2) = t^2 e^(-3t^2/4) into u' + (3/2)t u = (3/2)t^2 e^(-3t^2/4), with integrating factor e^(3t^2/4) and d/dt(e^(3t^2/4) u) computed.
1. Homework Statement

Posted

Homework Equations



Posted

The Attempt at a Solution


Posted

I just need the work to be checked.
 
My only comments are:
1. Your title is misleading; this is not a linear DE
2. Your answer should be an equation with ##y## and ##t##.
3. I won't comment on the steps because of the impossibility of editing images.
 
Ashley1nOnly said:
I integrated to get the last part.
Ashley1nOnly said:
View attachment 106286 1. Homework Statement
Posted

Homework Equations



Posted

The Attempt at a Solution


Posted

I just need the work to be checked.

I almost always avoid looking at posted images, but I can offer useful advice. If you have a differential equation and a (supposed) solution, the standard operating principle you should always apply is to check the solution for yourself, by substituting it into the differential equation and seeing if it "works".