1st Order Differential Equation - Power Series Method

  • #1

Homework Statement


upload_2018-10-26_11-27-21.png



The Attempt at a Solution


upload_2018-10-26_11-28-2.png


I have deliberately made several obvious steps, because I keep ending up here. However I have no idea what to do from here. I thought about the fact, that differential equations have the solution ##x = x_{HOM} + x_{Inhom}##, but the ##x_{HOM}## ends up the same, except equal 0, which suggests that the only solution is ##c_0 = -t \cdot sin(t)##. as all ##c_n=0, n \geq 1, t \in (0,\infty)##. But that can't be right, because that actually constitute a solution?
 

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  • #2
32
1
try writing ##sin(t)## as ##\sum_{0}^{\infty}\frac{(-1)^n t^{2n+1}}{(2n+1)!}##, simplify the expression and then try to find solutions for which the sum is always going to equal to zero
 

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