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I have a differential equation of the form

d^{2}x

---------------- = g/z * x(t)

dt^{2}

Here g and z are constants. So, this is a 2nd order ODE which has a closed form solution.

In fact, i know the solution for x in terms of cosh and sinh functions.

In the above differential equation, if z is not constant. That is, id the the eqn becomes

d^{2}x

---------------- = g/z(t) * x(t)

dt^{2}

Is it still correct to assume x is only a function of time?

If z(t) is sinusoidal, then this equation is a non-linear 2nd order ODE. Am i right?

Please point me to a standard textbook which might help me solve these kind of non-linear diff.equations? Any suggestions/pointers are welcome. Thank You in advance.

--MB

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# Help toward solving second order non-linear differential equation

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