Using the two partial differential equations construct a partial differential equation containing only variable 'G' and solve it.

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The two equations are: $$a\frac{\partial R}{\partial x} + bR = cG \rightarrow (1)$$ $$d\frac{\partial^2 R}{\partial x^2} + eG = f\frac{\partial R}{\partial t} \rightarrow (2)$$ where a,b,c,d,e and f are constants. 'R' and 'G' are functions of independent variables 'x' and 't'.

Using equations (1) and (2) construct a partial differential equation containing only variable 'G'. If possible also give the solution for the same equation.

Can the constructed partial differential equation in terms of 'G' be modified to get the Korteweg-de Vries equation ?

This is the wikipedia link for Korteweg-de Vries equation: https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation