## 385 Reputation

11 years, 114 days

## Plotting a solution of an ode...

Maple 17

r(t) = RootOf(Int(_a/sqrt(-4*_a^4+5*_a^2-1), _a = 1 .. _Z)+t), r(t) = RootOf(Int(_a/sqrt(-4*_a^4+5*_a^2-1), _a = _Z .. 1)+t), r(t) = RootOf(Int(_a/sqrt(-4*_a^4+13*_a^2-9), _a = 1 .. _Z)+t), r(t) = RootOf(Int(_a/sqrt(-4*_a^4+13*_a^2-9), _a = _Z .. 1)+t)

ist my result of an ODE

g := dsolve([oder, r(0) = 1, (D(r))(0) = 0])

oder := diff(r(t), t, t) = 4*sqrt(1-(diff(r(t), t))^2)+(1-(diff(r(t), t))^2)/r(t)

Now usually maple gives me one solution, so I can just plot with

## simplify expression...

Maple 17

-(1/2*I)*(I*Pi*ln(2)-I*Pi*ln(g+4)-2*ln(2)^2+2*ln(2)*ln(g+4)-2*ln(2)*ln(-1/2*I)+ln(g+4)*ln(-1/2*I)-ln(g+4)*ln(2*I)+ln(-1/2*I)*ln(4-g)+ln(4-g)*ln(2*I))/Pi

why doesnt maple simplify this expression any further?

but he complains when using combine saying:

Error, (in combine/ln) second argument must be a maple type

Why is that?

## calculating with lists...

Maple 17

i have a list of numeric values like this:

r:=[a,b,c,....]

now i want to calculate the quantity

s:=lambda-r^2

which in turn should give me a list again whose entries are:

[lambda-a^2,lambda-b^2,...]

but just doing

s:=lambda-r^2 doesnt work.

lambda is an arbitrary number

## dsolve invalid input when plotting...

Maple 17

ode := diff(x(t), t, t) = 1^2*(cosh(x(t))-1)/cosh(x(t))

ics := x(0) = 2, (D(x))(0) = 0

xs := dsolve({ics, ode})

plot(xs, t = 0 .. 3)

why do i get this error?

Error, invalid input: plot expects its 1st argument, p, to be of type {set, array, list, rtable, algebraic, procedure, And(`module`, appliable)}, but received x(t) = RootOf(Int(1/(-4*arctan(exp(_a))+4*arctan(exp(2))-4+2*_a)^(1/2), _a = _Z .. 2)+t)

## Defining an algebra...

How do I define an algebra in Maple?

Say for example Quaternions:

i^2=j^2=k^2=i*j*k=-1

Thx

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