MHB Finding a value for a y(0) = a in a IVP

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To solve the initial value problem defined by the equation (xy' + y)/(1 + x^2y^2) = 1 with the condition y(0) = a, it is necessary to find a value of a that keeps the equation defined. The discussion suggests starting with an implicit solution for the differential equation, acknowledging the need to clarify the equation's structure. A proposed substitution is u = xy, leading to u' = y + xy', which may facilitate finding the solution. The conversation highlights the importance of ensuring that the chosen value of a does not lead to undefined conditions in the equation. Ultimately, the goal is to determine the maximal solution for the initial value problem.
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Find the value of a ∈ R for which the initial value problem:

(S) {(xy' +y)/(1+x2y2)=1
{y(0)= a

has a solution and, for this value of a, find explicitly the maximal solution of (S).

I'm assuming I first find the implicit solution of the original diff eq (which I'm not too sure how to do given the equation) and then find a number a which will not make the eq undefined? I'm not too sure how to go about this one.
 
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You have some derivatives in an expression there, but it's not a differential equation, because there's no equals sign. Is there more to the expression?
 
My apologies, it is equal to 1, will edit original post to include that.
 
Try the substitution $u=xy$. Then $u'=y+xy'$. Can you continue?
 

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