- #1

- 986

- 9

## Homework Statement

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

(a) y'=(2x)/(y+x

^{2}y), y(0)=-2

## Homework Equations

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

## 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: