# How do I interpret an error message from DSolve?

I am trying to find non-trivial solutions of the ODE $\lambda u'(x) = u(x+R) - u(x)$ using Mathematica.

In particular, I am using the command

 DSolve[a*y'[x] == y[x + r] - y[x], y[x], x]


which for a standard (i.e., non-delayed, non-anticipated ODE) works fine.

In this case I got the error

DSolve::litarg: "To avoid possible ambiguity, the arguments of the dependent variable in !({a\\ *SuperscriptBox[\"y\", \"[Prime]\", MultilineFunction->None][x] == (-y[x]) + y[r + x]}) should literally match the independent variables."

• Have you read the documentation yet? Dec 23, 2012 at 16:55
• @Mr.Wizard, sorry, thanks for the doc link. Indeed I googled the error; although I found general answers which I am too newbie o be able to uderstand. Be patient. Dec 23, 2012 at 17:00
• @Mr.Wizard that doc page doesn't really help solve the DDE
– acl
Dec 23, 2012 at 17:04
• I suggest you look at this doc page Dec 24, 2012 at 0:56

This is a delay differential equation, not an ODE. Mathematica can numerically solve DDEs with constant delays, eg, scaling u and x to reduce your DDE to $u'(x)=u(x+1)-u(x)$, we can do
sln = NDSolve[{u'[x] == u[x - 1] - u[x],