Question: Differential equations

For the valuation of a storage facility you get the equation \(\frac{1}{2} \sigma^{2} V^{\prime \prime}+\alpha(\bar{P}-\) \(P) V^{\prime}-r V=c P\), where \(\sigma, \alpha, \bar{P}, c, r\) are constant and \(V: \mathbb{R} \rightarrow \mathbb{R}\) is a function

of the variable \(P\). For simplicity, let us say that \(\frac{1}{2} \sigma^{2}=1\) and \(\alpha=0\) and so that you only need to solve

Find the general solution \(V(P)\) of this equation.

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