What is the solution for (dy)/(dx)=(4x^2)/(sqrt(4+x^3)) ?

The solution for (dy)/(dx)=(4x^2)/(sqrt(4+x^3)) is y= 8/3 sqrt(4+x^3)+c_{1}

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(dy)/(dx)=(4x^2)/(sqrt(4+x^3))

\frac{d y}{d x} = \frac{4 x ^{2}}{4 + x ^{3}}

y = \frac{8}{3} 4 + x^{3} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{4 x ^{2}}{4 + x ^{3}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{4 x ^{2}}{4 + x ^{3}}

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

then

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

y = \int \frac{4 x ^{2}}{4 + x ^{3}} d x

\int \frac{4 x ^{2}}{4 + x ^{3}} d x = \frac{8}{3} 4 + x^{3} + c_{1}

y = \frac{8}{3} 4 + x^{3} + c_{1}

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What is the solution for (dy)/(dx)=(4x^2)/(sqrt(4+x^3)) ?
The solution for (dy)/(dx)=(4x^2)/(sqrt(4+x^3)) is y= 8/3 sqrt(4+x^3)+c_{1}