A Linear Approximation of the Non-linear Modified Langumir and Van der Pol Differential Equations by the Application of the Generalized Sundman Transformation

The non-linear ordinary differential equations of Langumir and Van der Pol are challenging to solve analytically. Thus, this work aims to convert these non-linear equations into linear form so that they may be easily solved. Assuming that the coefficients of the two equations meet the linearizability requirements, they are presented in the appropriate linearizable formats. After achieving this, the generalized Sundman transformation was used to linearize the equations. The formulae defines the nonpoint transformation known as the generalized Sundman transformation (GST). Basic solutions for the two equations were obtained upon application of the GST. The conventional approach of variation of parameters was used to solve the linear equations that emerged from the linearization process.