Non-homogenous secx ODE's and Euler eq's

[hivesaeed4]

Suppose we have Asec(x) on the right hand side in a non-homogenous ODE and in a Euler equation. How do we solve it? ( I know how to solve for cos and sin on the right hand side but not for any other trig function).

 

[hivesaeed4]

Help?

 

[miglo]

For non-homogeneous ordinary differential equations, i was taught that you always had to use the method of annihilators if the right hand side was either cos(x), sin(x), exp(x), a polynomial function or the product and sum of any of these functions. For functions like sec(x)=1/cos(x) the annihilator method won't work, and therefore you will need to use the variation of parameters method to solve your differential equation.

It's how i was taught, so i don't know if there is another method out there that could be used.

 

[BackEMF]

Non-homogeneous secx eh? :P

You could always try a Power Series solution if you expand the sec(x) in a power series:

http://en.wikipedia.org/wiki/Power_series_solution_of_differential_equations

 

[blue_raver22]

Non-homogenous ODEs and Euler equations can be solved using a variety of methods, depending on the specific form of the equation. In the case of Asec(x) on the right hand side, there are a few possible approaches that can be used.

One method is to use the substitution u = sec(x) to transform the equation into a separable form, and then solve using standard techniques for solving separable ODEs.

Another approach is to use the method of variation of parameters, where we assume a solution of the form y = u(x)sec(x), and then use this to find a particular solution to the non-homogenous equation.

In the case of a Euler equation, we can use the substitution u = ex to transform the equation into a more manageable form, and then solve using techniques for solving linear ODEs.

It is also worth noting that depending on the specific problem and context, numerical methods such as Euler's method or Runge-Kutta methods may also be useful for solving non-homogenous ODEs and Euler equations.

In summary, there are multiple methods that can be used to solve non-homogenous ODEs and Euler equations with Asec(x) on the right hand side. The best approach will depend on the specific form of the equation and the context of the problem.