(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the solution to each of the following initial value problems in explicit form.

(a) y'=(2x)/(y+x^{2}y), y(0)=-2

2. Relevant equations

Uhhhhh I suppose it would be relevant to mention that an equation in the form dy/dx = g(x)h(y) is separable

3. The attempt at a solution

y'=(2x)/(y+x^{2}y)=[1/y][2x/(1+x^{2})]

==> y dy=2x/(1+x^{2}) dx

==> y^{2}/2 + C_{1}= ln|1+x^{2}| + C_{2}

==> y^{2}/2 = ln|1+x^{2}| + C (C = C_{2}- C_{1}, just to combine into one constant)

==> (-2)^{2}/2 = ln|1+0^{2}| + C

==> C = 2

==> y^{2}= 2ln|1+0^{2}| + 4

==> y = +/- √(2ln|1+x^{2}| + 4)

That just seems a little too complicated an answer. :yuck:

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# Please check my diffy q

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