What is the solution for y^2((dx)/(dy))+y^3=1 ?

The solution for y^2((dx)/(dy))+y^3=1 is x=-1/y-(y^2)/2+c_{1}

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y^2((dx)/(dy))+y^3=1

y^{2} (\frac{d x}{d y}) + y^{3} = 1

x = - \frac{1}{y} - \frac{y ^{2}}{2} + c_{1}

Solution steps

y^{2} (\frac{d x}{d y}) + y^{3} = 1

Substitute

\frac{d x}{d y}

with

x^{'} (y)

y^{2} (x^{^{'}} (y)) + y^{3} = 1

Isolate

x^{'} (y) : x^{'} (y) = \frac{1 - y ^{3}}{y ^{2}}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

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

\int \frac{1 - y ^{3}}{y ^{2}} d y = - \frac{1}{y} - \frac{y ^{2}}{2} + c_{1}

x = - \frac{1}{y} - \frac{y ^{2}}{2} + c_{1}

\int \frac{x ^{2}}{x ^{2} + 1} d x

7 x e^{x}

\int cos (8 x) cos (5 x) d x

\frac{d}{d x} (\frac{5 x}{3})

What is the solution for y^2((dx)/(dy))+y^3=1 ?
The solution for y^2((dx)/(dy))+y^3=1 is x=-1/y-(y^2)/2+c_{1}