Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}=\frac{2x}{3y^2}$

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Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=\frac{2x}{3y^2}$

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}=\frac{\frac{2}{3}x}{y^2}$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(2x)/(3y^2). Take \frac{2}{3} out of the fraction. Simplify the fraction \frac{\frac{2}{3}x}{y^2}. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final Answer

$y=\sqrt[3]{x^2+2C_0}$
$\frac{dy}{dx}=\frac{2x}{3y^2}$

Related formulas:

2. See formulas

Time to solve it:

~ 0.13 s (SnapXam)