- #1

- 198

- 22

## Homework Statement

[itex]\frac{dy}{dx} = y^{\frac{2}{3}}[/itex] with y(0) = y

_{0}

## Homework Equations

## The Attempt at a Solution

after separating variables:

[itex] \frac{dy}{y^{\frac{2}{3}}} = dx [/itex]

then integrating:

[itex] 3y^{\frac{1}{3}} = x + c [/itex]

and rearranging:

[itex]y(x) = \left( \frac{x + c}{3} \right)^{3}[/itex]

after solving for initial value, y(0) = y

_{0}:

c = 3y

_{0}

^{1/3}

therefore

[itex]y_{0} = \left( \frac{c}{3}\right)^{3}[/itex]

is that what they're asking for? I believe that would give a unique solution, no? also the question is explicit with value

**s**is this plurality given by the constant c?

Last edited: