# How do you solve the differential dy/dx=10x^2/√1+x^3?

s2vunov 2022-09-29 Answered
How do you solve the differential $\frac{dy}{dx}=\frac{10{x}^{2}}{\sqrt{1+{x}^{3}}}$?
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## Answers (1)

recepiamsb
Answered 2022-09-30 Author has 9 answers
We know that
$\frac{d}{dx}\left(\sqrt{1+{x}^{3}}\right)=\frac{3}{2}\frac{{x}^{2}}{\sqrt{1+{x}^{3}}}$
so, grouping variables
$dy=\frac{20}{3}\frac{d}{dx}\left(\sqrt{1+{x}^{3}}\right)dx$ integrating
$y=\frac{20}{3}\sqrt{1+{x}^{3}}+C$
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