# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=e^(2x+3y). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. 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\frac{1}{e^{3y}}dy and replace the result in the differential equation.

$y=\frac{\ln\left(-3\left(\frac{1}{2}e^{2x}+C_0\right)\right)}{-3}$

### Problem Analysis

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

### Main topic:

Differential equations

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