I was wondering if there were any methods to compute solutions for equations of the type $$\sum_{n=0} ^{\infty} a_n y^{(n)}=F(y,x)$$ I do not believe exact solutions would be easy or possible to find, but perhaps series solutions would be less unwieldy. I have searched online for information but could only find research papers available solely through a purchase and other documents that elaborated very little on finding solutions. What are some fields related to these problems and where can I find information on them?
Methods to solve differential equations of infinite order?
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