What is the (dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1 ?

The (dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1 is 1/(1-2x)

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(dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1

\frac{d y}{d x} = \frac{y ^{3}}{1 - 2 x y ^{2}}, y (0) = 1

\frac{1}{1 - 2 x}

Solution steps

\frac{y ^{3}}{1 - 2 x y ^{2}} = \frac{y ^{3}}{1 - 2 x y ^{2}}

Constant function results in a constant

y (0) = 1

= \frac{1 ^{3}}{1 - 2 x \cdot 1 ^{2}}

Simplify

\frac{1 ^{3}}{1 - 2 x \cdot 1 ^{2}} : \frac{1}{1 - 2 x}

= \frac{1}{1 - 2 x}

What is the (dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1 ?
The (dy)/(dx)=(y^3)/(1-2xy^2),y(0)=1 is 1/(1-2x)