Hi

A function ta(x) is defined

Testing it indicates  that everything seems ok.

ta(2010);                 0.2212273448

ta(2050);               4.440420849

But printing goes totally wrong :

plot(ta(x), x = 2000 .. 2030);

The code consists of 13 constants and 4 equations.

Am I overlooking something?  Any idea?

na := 8.069439677916595*10^5;
nb := -1.777065899098942*10^3;
nc := 1.467451715287991;
nd := -5.383733471268420*10^(-4);
ne := 7.404613067985871*10^(-8);
am := 0.77317633747818500000;
bm := -0.00626025741156560000;
cm := 0.00002185947833342660;
ap := 471.909671218139000000000000;
bp := -7.368938071612570000000000;
cp := 0.041111235018593800000000;
dp := -0.000098963929768727000000;
ep := 0.88147417256725300*10^(-7);

c_y := y -> na + nb*y + nc*y^2 + nd*y^3 + ne*y^4;
to_c := ppm -> ap + bp*ppm + cp*ppm^2 + dp*ppm^3 + ep*ppm^4;
to_y := y -> tpn(c_y(y));
ta := x -> 0.0014*int(to_y(y), y = 2000 .. x);

I have defined a function pp(x).  It plots correctly 

but pp(2020); should return 410, and it returns 98000. Maybe I am doing something stupid, but I just can't figure out what!

a := 0.340699639252428*10^13;
b := -0.118229737138742*10^11;
c := 0.175816922773262*10^8;
d := -14523.7138112711;
e := 7.19782673654200;
f := -0.00214008825847444;
g := 0.353463615941623*10^(-6);

h := -0.250170509163729*10^(-10);

pp := x -> a + b*x + c*x^2 + d*x^3 + e*x^4 + f*x^5 + g*x^6 + h*x^7;

plot([pp(x)], x = 1960 .. 2100, gridlines = true, size = [900, 600])

Syrup has awsome functionality but it only installs halfway.  I have tried to run Maple as administrator and install from File - Open From Cloud. Is there a better way ?

Charging a capacitor with a DC is well known and interaction with a sinusoidal signal is known to perfection.

The mathematical solutions behind an arbitrary waveform V1(t) is hard or impossible? to find .

To simplify, the arbitrary wave can be expressed with a 2-d degree polynom. This gives a fairly simple

expression with an integral. The problem however is that V2(t) - the capacitor voltage - appears on both sides and maple seems unable to resolv this into a symbolic expression.

If this can be solved it would be great ! The solution should be of the symbolic form V2(a,b,c,V2start,t1,t2,RC) and give the answer what voltage the capacitor V2 would reach arter charging between t1 and t2  with a V1(t) that is changing during charge.