abcalphabeta Posted September 21, 2010 Share Posted September 21, 2010 i keep getting stuck in some problems of physics because the differential equation of the form a dy/dx + by = c f(x) keeps cropping up. is there any general method to solve this differential equation? when f(x) is sinusoidal, we avoid it using j operators and get the solution but in my particular problem f(x) is exponential. Link to comment Share on other sites More sharing options...
the tree Posted September 27, 2010 Share Posted September 27, 2010 Yes, there is a general approach. More than one less-than-general approach. You may wish to Google around for "(first order) inhomogenous linear ODEs". In this case, the important thing is that a sum of solutions to an ODE, is a solution to that ODE. So for the most general answer you will want to give. y(x) = u(x) + v(x) Where u(x) is the a y(x) that satifies LHS=0 (the implicit sol'n). And v(x) is a y(x) that satisfies y(x)=RHS and LHS=RHS (the particular sol'n). Link to comment Share on other sites More sharing options...
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