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

nathancurtis11

New member
Sep 3, 2013
10
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.
 
Last edited:

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
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?
 

nathancurtis11

New member
Sep 3, 2013
10
My apologies, it is equal to 1, will edit original post to include that.
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
Try the substitution $u=xy$. Then $u'=y+xy'$. Can you continue?