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

#### nathancurtis11

##### New member
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
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
My apologies, it is equal to 1, will edit original post to include that.

#### Ackbach

##### Indicium Physicus
Staff member
Try the substitution $u=xy$. Then $u'=y+xy'$. Can you continue?