# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{dy}{dx}=\frac{4y}{xy-3x}$

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

$dy\left(xy-3x\right)=4ydx$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(4y)/(xy-3x). Apply fraction cross-multiplication. Factoring by x. 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.

$y-3\ln\left(y\right)=4\ln\left(x\right)+C_0$

### Problem Analysis

$\frac{dy}{dx}=\frac{4y}{xy-3x}$

### Main topic:

Differential equations

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