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... some simple analytical ways solving ordinary differential equations (Part 2)

Sample 21:

The following example is not meant for those, which have an appointment
with a nice girl within the next 1 hour or so. But if you are desperate to
find an excuse allowing you not to participate at all in the looming tea-party
with your not-so-much-loving mother-in-law, then feel absolutely free to join
me in the problem represented by our example 21.

This statement above purely reflects the opinion of the author.
A similarity with any living mother-in-law is purely unintentional.

Now, lets finally let the mother-in-law topic generously behind us.

dg23

We will choose c₁ = 2

`:f:/f.txt 0: ,/'" ",''$+{(2*x-0.5)+(0.5*1+x*x)+(steps -4 4 30)*exp (-x)}'steps -2 7 30

Sample 22:

dg25

We will choose c₂ = 1

`:f:/f.txt 0: ,/'" ",''$+{((steps -2 2 30)*exp 2*x)+(1+x*-1+x*x)*exp 5*x}'steps -1.3 0.3 30

Sample 23:

dg26

We will choose c₂ = 1

`:f:/f.txt 0: ,/'" ",''$+g'steps -3 3 40

where

g:{(p*steps -2.25 2.25 30)+(sin q)+((3f*x*p:cos q)-sin 2f*q:2f*x)%24f}

Sample 24:

dg27

We will choose c₂ = 1

`:f:/f.txt 0: ,/'" ",''$+{-0.5+(exp -1f*x)+(-0.1*cos 2*x)+(steps -2 6 30)*exp x}'steps -3.1 3.1 30

Sample 25:

dg28

We will choose k₂ = 1

`:f:/f.txt 0: ,/'" ",''$+{(s*steps -7 0 30)+c+0.01*(exp d)*((7-10*x)*c:cos d)+
(-1+5*x)*s:sin d:2*x}'steps -1.7 2.3 30

Sample 26:

dg30

Sample 27:

dg31

(*) Leonhard Euler (born 15.Apr.1707 Basel,Switzerland, died 18.Sep.1783 St.Petersburg, Russia)

We will choose K₂ = 1

`:f:/f.txt 0:,/'" ",''$+{x*(steps -6 -3 30)+(log x)+0.75*x*x}'steps 0.01 3 30

Sample 28:

dg32

and we will choose C^*₂ = 1

`:f:/f.txt 0:,/'" ",''$+{((steps -70.2 70.2 50)*cos l)+(sin l)+l*cos l:log x}'
steps 0.00001 3100 100

Sample 29:

We come now to the end of this chapter..and close it with a trivial example from
a system of linear diff eq. with constant coefficients
dg33

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