Linear differential equation hwk check

Ashley1nOnly
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1. Homework Statement

Posted

Homework Equations



Posted

The Attempt at a Solution


Posted

I just need the work to be checked.
 
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I integrated to get the last part.
 
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".
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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