1. ## Differential Questions

Solve:

$\frac{dy}{dx}= \frac{y^3}{1-2xy^2},\ \ y(0)=1$

No idea how to do this, tried various methods and came up with nothing. Any Suggestions on how to attempt this one?

2. Originally Posted by electricalphysics
Solve:

$\frac{dy}{dx}= \frac{y^3}{1-2xy^2},\ \ y(0)=1$

No idea how to do this, tried various methods and came up with nothing. Any Suggestions on how to attempt this one?
If you re-write your ODE as

$
\frac{dx}{dy} = \frac{1-2xy^2}{y^3}
$

or

$
\frac{dx}{dy} + \frac{2x}{y} = \frac{1}{y^3}
$

it's linear in $x$.

3. or divide top and bottom by $y^3$ and put $y=tx$ to turn your equation into a separable one.

4. Originally Posted by Danny
If you re-write your ODE as

$
\frac{dx}{dy} = \frac{1-2xy^2}{y^3}
$

or

$
\frac{dx}{dy} + \frac{2x}{y} = \frac{1}{y^3}
$

it's linear in $x$.
Thanks i got it, but
When am I to know I must flip the dy/dx to make x(y)? Is it because of the particular form of the ODE ?

5. Originally Posted by electricalphysics
Thanks i got it, but
When am I to know I must flip the dy/dx to make x(y)? Is it because of the particular form of the ODE ?
When it works! Many mathematics problems are solved by "try this and if it doesn't work try that". The important thing is to try.