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I'm stuck as to where to start with this question:

The position function x(t) in a certain nonlinear system is described by the second order ODE:

< equation.gif >

Transform this ODE into a pair of first order ODEs for x1=x and x2=dx/dt. (Note that x2 represents the velocity in this system.)

I've thought about calculating the homogeneous equation and then the particular integral, but (a) how is this done with a sin(dx/dt) on the RHS and (b) how does this yield a pair of solutions? Or is there another way to go about it?

The position function x(t) in a certain nonlinear system is described by the second order ODE:

< equation.gif >

Transform this ODE into a pair of first order ODEs for x1=x and x2=dx/dt. (Note that x2 represents the velocity in this system.)

I've thought about calculating the homogeneous equation and then the particular integral, but (a) how is this done with a sin(dx/dt) on the RHS and (b) how does this yield a pair of solutions? Or is there another way to go about it?