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# Mathematica only rewrites the differential equation

Posted 10 years ago
 Hi, So i am trying to solve this differential equation. However when i press shift+enter Mathematica just rewrites the equation, not giving an answer. I would like to graph the result aswell. This is what it looks like: Equation1 = Dsolve[{L''[ t] == (((0.01*4 \[Pi]*10^-7* L[t]*(440*e^(-t/(0.5*0.0025)))^2/\[Pi])*(0.01^2 + (L[t]^2 - L[t]*Sqrt[0.01^2 + L[t]^2]))/Sqrt[0.01^2 + L[t]^2])/ 0.01), L[0] == 0.001, L'[0] == 0.01}, L, {t, 0, 0.1}]  And it gives me the answer: Dsolve[{(L^\[Prime]\[Prime])[t] == ( 0.07744 e^(-1600. t) L[t] (0.0001 + L[t]^2 - L[t] Sqrt[0.0001 + L[t]^2]))/Sqrt[ 0.0001 + L[t]^2], L[0] == 0.001, Derivative[1][L][0] == 0.01}, L, {t, 0, 0.1}]  which is basically only a rewriting... what should i do to solve it? I am new to mathematica so i guess it is a typing-error somewhere, can anyone assist me? I attach the file below if you want to try yourself and my goal is to find the L. Regards Mattias Pettersson :) Attachments:
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Posted 10 years ago
 Hi Mattias,there are several problems with your input: The Function DSolve is written with a capital S. The function you want to use here is NDSolve. You use e^ which is not correct. e is either Exp[1] or you wrap Exp around the exponent or you use the special symbol or use E, but not simply e. This piece of code should work: Equation1 = NDSolve[{L''[t] == (((0.01*4 ?*10^-7*L[t]*(440*Exp[1]^(-t/(0.5*0.0025)))^2/?)*(0.01^2 + (L[t]^2 - L[t]*Sqrt[0.01^2 + L[t]^2]))/ Sqrt[0.01^2 + L[t]^2])/0.01), L[0] == 0.001, L'[0] == 0.01}, L, {t, 0, 0.1}] You can plot it like so: Plot[L[t] /. Equation1, {t, 0, 0.1}] which givesCheers, Marco
Posted 10 years ago
 Okey, thanks a lot! But now a new problem arose... This expression is actually a rewritten formula derived from the characteristics of an electromagnetic railgun. The railgun fires a projectile, the L being distance from the start point at a time t, the velocity of it at that time is the L' and so on... But how can the L be linear? and the velocity negative at some instances? It does not make any sense.. Can anyone help? It might be that Mathematica does not understand the t in this part: (440*E^(-t/(0.5*0.0025))) maybe Mathematica does not understand that t is the time, just a new variable since it is not in []? Thanks a lot Mattias
Posted 10 years ago
 Dear Mattias,no that is not the problem, I believe. I think that Mathematica treats your equation quite correctly. The solution looks rather straight because of your parameters. If you use different parameters: Equation1 = NDSolve[{L''[ t] == (((0.1*4 ?*10^-1* L[t]*(440*Exp[1]^(-0.001 t/(0.5*0.0025)))^2/ ?)*(0.01^2 + (L[t]^2 - L[t]*Sqrt[0.01^2 + L[t]^2]))/ Sqrt[0.01^2 + L[t]^2])/0.01), L[0] == 0.1, L'[0] == 0.01}, L, {t, 0, 0.1}] looks not that linear anymore:I think that for your parameters the straight line is a good approximation in your domain, but the result is strictly speaking not a straight line.Cheers, Marco