How do you solve the differential $\frac{d y}{d x} = \frac{10 x^{2}}{\sqrt{1 + x^{3}}}$ $dy/dx=(10x^2)/sqrt(1+x^3)$ ?

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Answer 1 · 2016-11-19T00:24:50

$y = \frac{20}{3} \sqrt{1 + x^{3}} + C$ $y = 20/3 sqrt(1+x^3)+C$

We know that

$\frac{d}{d x} (\sqrt{1 + x^{3}}) = \frac{3}{2} \frac{x^{2}}{\sqrt{1 + x^{3}}}$ $d/dx(sqrt(1+x^3))=3/2 x^2/sqrt(1+x^3)$

so, grouping variables

$d y = \frac{20}{3} \frac{d}{d x} (\sqrt{1 + x^{3}}) d x$ $dy =20/3d/dx(sqrt(1+x^3))dx$ integrating

$y = \frac{20}{3} \sqrt{1 + x^{3}} + C$ $y = 20/3 sqrt(1+x^3)+C$

How do you solve the differential dy/dx=(10x^2)/sqrt(1+x^3)dydx=10x2√1+x3dy/dx=(10x^2)/sqrt(1+x^3)?