Find the particular solution of the differential equation `log ((dy)/(dx))=3x+4y` given that `y = 0` when `x = 0`.

Explanation

To find the particular solution of the differential equation \( \log\left(\frac{dy}{dx}\right) = 3x + 4y \) given that \( y = 0 \) when \( x = 0 \), we will follow these steps:

### Step 1: Rewrite the equation
Start by exponentiating both sides of the equation to eliminate the logarithm:
\[ \frac{dy}{dx} = e^{3x + 4y} \]
This can be rewritten using the property of exponents:
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