# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=\frac{\left(3x^2\right)}{y^2}$

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

$y^2dy=3x^2dx$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(3x^2)/(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, the left side with respect to y, and the right side with respect to x. Solve the integral \int y^2dy and replace the result in the differential equation. Solve the integral \int3x^2dx and replace the result in the differential equation.

$y=\sqrt[3]{3x^{3}+C_1}$

### Problem Analysis

$\frac{dy}{dx}=\frac{\left(3x^2\right)}{y^2}$

### Main topic:

Differential equations

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