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$$\begin{cases} \frac{dy}{dx} + 3y = 8, \\ y(0) = 0. \end{cases}$$

So, I have been getting an answer of $3$ by integrating and getting $\ln(8-3y) = x$ and solving. But my book says the answer must be expressed as a function of $x$. I do not know what to do.

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    The standard procedure is: you find a particular solution to the ODE (in this case there is a constant solution), and the general solution to the corresponding homogeneous ODE, which here has the form $y = c*something(x)$. Then you find $c$ so c*something(0) + [particular solution](0) = 0$2012-10-04
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    This problem will admit separation of variables.2012-10-04

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