Dsolve: assigning constants of integration and subscripts

[KleZMeR]

I have an equation I am solving with Mathematica:

In:

DSolve[y''[t] +
Subscript[\[Omega], c]^2 y[
t] == -Subscript[\[Omega], c]^2 Subscript[v, d]*t +
Subscript[\[Omega], c]*Subscript[v, 0], y[t], t]

Out:

{{y[t] ->
C[2] Cos[t Subscript[\[Omega], c]] +
C[1] Sin[t Subscript[\[Omega], c]] + (
Subscript[v, 0] - t Subscript[v, d] Subscript[\[Omega], c])/
Subscript[\[Omega], c]}}



I would like to replace the two constants of integration(C[1], C[2]) with two chosen variables

If I include this with the DSolve command:

{C[1] -> (Voy/omega), C[2] -> ((Voy-Vd)/omega)},

it returns that I can not use these for variables.

I have also found a GeneratedParameters-> function, but it does not work either,.. and if I'm correct, the GeneratedParameters-> Module{C[1], C[2]..&} function is only to ensure that C[] values are all unique, and does not change their representation.


I am also wondering how to change the subscript of Vo into Voy, Mathematica is not letting me do this.

Again, any help would be appreciated
Thanks

 

[CompuChip]

You can replace the parameters all the way at the end:

DSolve[ ..., y[t], t] /. {C[1] -> ..., C[2] -> ...}

and that works well for me.

When you type V_0y Mathematica sees the subscript as an expression, and replaces 0*y by 0 (which is usually very handy, but not what you want now). You can use o (letter oh) instead of 0 (number zero) in the subscript, or put it in a string: V_"y,0".

 

[Dale]

Or you can use

GeneratedParameters -> ((Voy - (# - 1) Vd)/omega &)

 

[CompuChip]

And of course the neatest solution is to just get them from the equation by plugging in the right boundary conditions:

DSolve[{equation, y'[0] == v0y, y[0] = 0}, y[t], t]

or something like that.