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

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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?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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