Can anyone check my work? 1st Order ODE Initial Value Problem

MustangGt94
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Homework Statement



dy/dt + ty/(1+t^2) = t/(1+t^2)^1/2 y(1) = 2

Need to solve this initial value problem. The equation is a 1st order ODE

Homework Equations





The Attempt at a Solution



I've attached my solution to the problem. Just wondering if anyone can check my work. I solved the problem using the Integrating factor method u(t).

Thank You!
 
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Thread 'Finding the nth roots of a complex number'

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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