How to solve some "tricky" differential equations

I'm a Mathematica user who is starting to learn MATLAB. My professor told me that if I want to do something serious, nothing is better than MATLAB. So, I have several DEs problems to solve.

First problem:

In Mathematica, I use this code for the solution of above equation

Second problem:

The Mathematica code

Third problem:

The code

I have consulted to MATLAB documentations how to solve above differential equations but I couldn't find the answer. Any help would be appreciated. Thank you.

Answer 1

[Torsten]

It should be possible to solve the first problem with MATLAB's "dsolve". Otherwise, rewrite you 3rd order ODE as a system of three first-order ODEs

y1'=y2
y2'=y3
y3'=y1+1

and use ODE45 to solve.

For the second and third problem, use DDE23.

Best wishes

Torsten.

[Deco Sukan]

In the first problem, I am having trouble to put the initial conditions into the codes. All the examples I know using "trivial" conditions, e.g. y(0)=0, y'(0)=1, y''(0)=2, ...

In the second and third problems, I have difficulties with the non-identical delays. In the second problem: x(t-2) and x(t-3), and in the third problem: x(t-1) and x(t-2).

Instead of some hints, could you please post complete codes to solve one of the above problems?

[Torsten]

Using dsolve, you should have no trouble to insert boundary conditions at three different points. Using a numerical solver, try BVP4C and look at the example "threebvp".

For the second and third problem: DDE23 deals with non-identical (constant) delays.

Invest a little time - nothing is for free.

Best wishes

Torsten.