
#1
Jan3013, 07:16 AM

P: 160

Hi i have the differential equation
[itex]\frac{d^{2}}{dt^{2}}X(t) +(A+B\frac{sin^{2}(mt)}{mt})X(t)[/itex] I have tried by hnd to solve this and am getting knowhere does anyone know how to solve it and then plot X against t (where the constants A, B and m will be arbitrarily added), possibly using maple? I know that it is related to the mathieua equations and have found this. Thanks 



#2
Jan3013, 09:21 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,890

Do you need an "analytic" solution? If you just want to graph the solution, I would recommend a "RungeKutta" numerical solution.




#3
Jan3013, 09:35 AM

P: 160

I just want to get a X= f(t) equation that i can then plot, for t values




#4
Jan3113, 12:31 AM

P: 3,175

Solving time dependent differential equation and plotting
I guess you mean:
[tex]\frac{d^{2}}{dt^{2}}X(t) +(A+B\frac{sin^{2}(mt)}{mt})X(t)=0[/tex] In which case as always multiply by dX/dt [tex] 1/2 \frac{d}{dt}(\frac{dX(t)}{dt})^2 + (A+B\frac{sin^{2}(mt)}{mt})/2 \frac{d}{dt}(X^2(t)) = 0[/tex] Now there's a problem, you need to integrate by parts to get the next equation: [tex] 1/2 (\frac{dX(t)}{dt})^2 + (A+B\frac{sin^{2}(mt)}{mt})/2 X^2(t)  \int X^2(t)/2 (B\frac{d}{dt}( \frac{sin^{2}(mt)}{mt}) dt = E[/tex] So now we get a mixed differentailintegral equation, which I am not sure how to approxiamte. 



#5
Jan3113, 01:45 AM

P: 745

The solutions cannot be expressed as a combination of a finite number of usual functions. In similar cases, some special functions were defined in order to represent the solutions on a closed form (see the example below, in case of a simpler equation). As far as I know, it was not done in the case of your equation. So, do not expect to find an exact analytical equation X=f(t). Of course, this ODE can be solved and the result can be plot, thanks to numerical computation methods. Another way for Physicians is to replace the equation by another simpler one which can be analyticaly solved, if the physical phenomena can be modeled with some approximations on some limited ranges of the parameters. 


Register to reply 
Related Discussions  
Problem with solving differential equation to solve for time  Introductory Physics Homework  8  
Solution of a Differential equation (Linear, 1st order). x=dependent variable  Calculus & Beyond Homework  11  
Solving a twocomponent linear ODE system with timedependent connection matrix  Differential Equations  0  
Differential Equation  Plotting Phase Plane  Calculus & Beyond Homework  21  
[Q] Some confuse involving time dependent schrodinger equation and time uncertainty  Quantum Physics  5 