y'=x^2 ∛y решитееее пожалуйстааа. Created by tillemma. algebra-ru

y'=x^2 ∛y решитееее пожалуйстааа...

tillemma @tillemma

August 2022 1 8 Report

y'=x^2 ∛y
решитееее пожалуйстааа

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Ответ:

$y'=x^2\cdot \sqrt[3]{y}\\\\\\\dfrac{dy}{dx}=x^2\cdot \sqrt[3]{y}\\\\\\\int \dfrac{dy}{\sqrt[3]{y}}=\int x^2\, dx\\\\\\\dfrac{y^{\frac{2}{3}}}{\frac{2}{3}}=\dfrac{x^3}{3}+C\\\\\\\dfrac{3}{2}\cdot \sqrt[3]{y^2}=\dfrac{x^3}{3}+C\\\\\\y=\sqrt{\Big(\dfrac{2x^3}{9}+C\Big)^3}$

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