# Find the general solution for each differential equation. Verify that each solution satisfies the original differential equation. \frac{dy}{dx}=4e^{-3x}

Find the general solution for each differential equation. Verify that each solution satisfies the original differential equation.
$\frac{dy}{dx}=4{e}^{-3x}$
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Step 1: Given that to
Find the general solution for each differential equation. Verify that each solution satisfies the original differential equation.
$\frac{dy}{dx}=4{e}^{-3x}$
Step 2: Solve
The given differential equation is a type of Variable Separable differential equation.
So, to solve this type of differential equation we have,
$\frac{dy}{dx}=4{e}^{-3x}$
$dy=4{e}^{-3x}.dx$
Integrating both sides we obtain,
$\int dy=\int 4{e}^{-3}.dx$
$y=4\left[\frac{{e}^{-3x}}{-3}\right]+C$
$y=-\frac{4}{3}{e}^{-3x}+C$
$3y=-4{e}^{-3x}+3C$
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