What is the solution for (dy)/(dx)=(10x^2)/(sqrt(1+x^3)) ?

The solution for (dy)/(dx)=(10x^2)/(sqrt(1+x^3)) is y= 20/3 sqrt(1+x^3)+c_{1}

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(dy)/(dx)=(10x^2)/(sqrt(1+x^3))

\frac{d y}{d x} = \frac{10 x ^{2}}{1 + x ^{3}}

y = \frac{20}{3} 1 + x^{3} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{10 x ^{2}}{1 + x ^{3}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{10 x ^{2}}{1 + x ^{3}}

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

then

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

y = \int \frac{10 x ^{2}}{1 + x ^{3}} d x

\int \frac{10 x ^{2}}{1 + x ^{3}} d x = \frac{20}{3} 1 + x^{3} + c_{1}

y = \frac{20}{3} 1 + x^{3} + c_{1}

x = 15 - y^{2}, x = y^{2} - 3

\int_{0}^{\frac{π}{8}} arctan (2 x) d x

\frac{\partial}{\partial w} (w arctan (uv))

y^{^{''}} + 2 y - 1 (y^{^{'}}) 2 = y^{^{'}}

n = 1 \sum \infty 9

What is the solution for (dy)/(dx)=(10x^2)/(sqrt(1+x^3)) ?
The solution for (dy)/(dx)=(10x^2)/(sqrt(1+x^3)) is y= 20/3 sqrt(1+x^3)+c_{1}