My Math Forum Coupled ODEs with exponential nonlinearity

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 August 15th, 2013, 11:17 PM #1 Newbie   Joined: Dec 2012 Posts: 10 Thanks: 0 Coupled ODEs with exponential nonlinearity Hi I need to find two functions $Y(x)$ and $R(x)$ that satisfy the following non-linear ODEs: $Y''=6k exp{2Y} -4g^2 exp {2R}$ $R''=4k exp{2Y} -4g^2 e {2R}$ where $k$ and $g$ are some constants. In particular when $k=0$ the solutions are $exp{-Y}=\frac{2g}{c_1} cosh(c_1 x+x_1)$ $Y=R+c_2 x+c_3.$ Can anyone help me to find solutions in general? It may also be helpful to write equations in matrix form. Thanks in advance.

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