using dsolve, ways to get particular solution only?

Question

R. Paul Borthwick 2014-10-21

评论： Walter Roberson 2018-2-12

I am teaching an undergraduate Ordinary Differential Equations Class.

Working with non-homogeneous equations, (second order, linear)

Want to use dsolve to get a particular solution only.

Specifically:

sol=dsolve('D2y-5*Dy+6*y==exp(t)*cos(2*t)+exp(2*t)*(3*t+4)*sin(t)','t')

When executed, we get a result of both complimentary and particular solution.

Is there anyway to configure dsolve to present only the particular solution?

Thanks Paul

David Arnold 2018-2-12

I just tried this:

syms t y(t)
sol=dsolve(diff(y,t,2)-5*diff(y,t)+6*y==exp(t)*cos(2*t)+exp(2*t)*(3*t+4)*sin(t),t);
sol=simplify(sol);
yp=subs(sol,symvar(sol),[0,0,t])

Walter Roberson 2018-2-12

When you use the syms version as David shows, then in some situations it can help to add assumptions to variables. For example

   syms y(t)
   syms t nonnegative
   syms B
   assume(B>1)

Answer 1

Mischa Kim 2014-10-21

Paul, I am not aware of a setting that would allow you to print the particular solution, only.

You can, however, eliminate the general solution by hand. E.g.,

 sol = dsolve('D2y-5*Dy+6*y==exp(t)*cos(2*t)+exp(2*t)*(3*t+4)*sin(t)','t')
 sv  = symvar(sol);
 sol_par = subs(sol,sv,[zeros(1,numel(sv)-1) sv(3)])